Koszulity of cohomology = K(π,1)-ness + quasi-formality

L. Positselski

doi:10.1016/j.jalgebra.2017.03.022

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Koszulity of cohomology = K(π,1)-ness + quasi-formality

Journal of Algebra. 2017. Vol. 483. P. 188–229.

Посицельский Л. Е.

This paper is a greatly expanded version of [37, Section 9.11]. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented. In particular, we include a categorical interpretation of the “Koszulity implies K(π,1) $” claim, discuss the differences between two versions of Massey operations, and apply the derived nonhomogeneous Koszul duality theory in order to deduce the main theorem. In the end we demonstrate a counterexample providing a negative answer to a question of Hopkins and Wickelgren about formality of the cochain DG-algebras of absolute Galois groups, thus showing that quasi-formality cannot be strengthened to formality in the title assertion.Приоритетные направления: математика Язык: английский DOI Текст на другом сайте Ключевые слова: formality Galois cohomology Nonhomogeneous quadratic relations Conilpotent coalgebras Koszul duality t-Structures of derived type Massey products Quasi-formality Noncommutative homotopy theory Galois groupsПохожие публикации Произведения Масси и соотношения в когомологиях алгебр Стинрода Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108-153 В недавней работе В. М. Бухштабера и автора была введена новая структура в когомологиях алгебр Хопфа в терминах спектральной последовательности Бухштабера (Bss). В классической алгебре Стинрода A2 имеется важная подалгебра Хопфа A(1), когомологии которой давно известны. В настоящей работе обсуждаемая структура на этих когомологиях полностью вычислена.
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Добавлено: 13 октября 2021 г.О ВЫШКЕ Цифры и факты Руководство и структура Устойчивое развитие в НИУ ВШЭ Преподаватели и сотрудники Корпуса и общежития Закупки Обращения граждан в НИУ ВШЭ Фонд целевого капитала Противодействие коррупции Сведения о доходах, расходах, об имуществе и обязательствах имущественного характера Сведения об образовательной организации Людям с ограниченными возможностями здоровья Единая платежная страница Работа в Вышке ОБРАЗОВАНИЕ Лицей Довузовская подготовка Олимпиады Прием в бакалавриат Вышка+ Прием в магистратуру Аспирантура Дополнительное образование Центр развития карьеры Бизнес-инкубатор ВШЭ Образовательные партнерства Обратная связь и взаимодействие с получателями услуг НАУКА Научные подразделения Исследовательские проекты Мониторинги Диссертационные советы Защиты диссертаций Академическое развитие Конкурсы и гранты Внешние научно-информационные ресурсы РЕСУРСЫ Библиотека Издательский дом ВШЭ Книжный магазин «БукВышка» Типография Медиацентр Журналы ВШЭ Публикации http://www.minobrnauki.gov.ru/ Министерство науки и высшего образования РФ https://edu.gov.ru/ Министерство просвещения РФ https://elearning.hse.ru/mooc Массовые открытые онлайн-курсы НИУ ВШЭ1993-2026 Адреса и контакты Условия использования материалов Политика конфиденциальности Правила применения рекомендательных технологий в НИУ ВШЭ Карта сайта Редакторуwindow.__INITIAL_STATE__={"config":{"widgetPrefixURL":"\u002F","widgetPostfixURL":"\u002F","prefixURL":"\u002F","domain":"publications.hse.ru","hseURL":"https:\u002F\u002Fwww.hse.ru","serverBaseURL":"http:\u002F\u002Flocalhost:5000","clientBaseURL":"https:\u002F\u002Fpublications.hse.ru","ruVersion":true},"useTemplate":1,"article":{"id":"206613444","title":"Koszulity of cohomology = K(π,1)-ness + quasi-formality","href":"\u002Farticles\u002F206613444","type":"ARTICLE","issn":"0021-8693","eissn":"1090-266X","status":1,"is_hidden":0,"createdAt":"2017-06-07T11:50:35.957Z","creator":{"id":"73946","title":{"ru":"\u003Ca target=\"_blank\" href=\"\u002Forg\u002Fpersons\u002F73946\"\u003EЧудаева О. 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P. 188-229."},"cardVeryfy":{"overDate":false,"hasVerify":false,"verifyFinish":false},"documents":{"DEMO":null,"DOI":{"id":"1","href":"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jalgebra.2017.03.022"},"OTHER_URL":{"id":"1","href":"http:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0021869317302120","ext":null,"size":null},"CONTENT_DOCUMENT":null,"DOCUMENT":null,"COVER":null},"projects":[],"authorsByType":{"author":[{"id":"35825480","href":null,"enVersionStatus":"2","title":{"ru":"Посицельский Л. Е.","en":"Positselski L."},"reverseTitle":{"ru":"Л. Е. Посицельский","en":"L. Positselski"},"altName":"","otherName":"","properties":{"scopus":"https:\u002F\u002Fwww.scopus.com\u002Fauthid\u002Fdetail.uri?partnerID=HzOxMe3b&authorId=8536420000&origin=inward","rinc":"","orcid":"https:\u002F\u002Forcid.org\u002F0000-0001-8836-3911"},"worknow":false,"authorInstitution":false,"verifyStatus":{"articleCollections":false,"hasAttr":false,"attr":{"verified":false,"affiliation":false}}}],"leader":null,"resp_editor":null,"sci_editor":null,"cmn_editor":null,"translator":null,"make_editor":null,"trn_editor":null},"magazine":{"id":"57961963","title":{"en":"Journal of Algebra","ru":"Journal of Algebra"}},"year":2017,"annotation":{"ru":"\u003Cp\u003E\n\tThis paper is a greatly expanded version of \u003Ca href=\"http:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0021869317302120#br0370\"\u003E[37, Section 9.11]\u003C\u002Fa\u003E. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented. In particular, we include a categorical interpretation of the “Koszulity implies K(π,1)\u003Cmath\u003E\u003Cmo\u003E\u003Cmo\u003E” claim, discuss the differences between two versions of Massey operations, and apply the derived nonhomogeneous Koszul duality theory in order to deduce the main theorem. In the end we demonstrate a counterexample providing a negative answer to a question of Hopkins and Wickelgren about formality of the cochain DG-algebras of absolute Galois groups, thus showing that quasi-formality cannot be strengthened to formality in the title assertion.\u003C\u002Fp\u003E\n","en":"\u003Cp\u003E\n\tThis paper is a greatly expanded version of \u003Ca href=\"http:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0021869317302120#br0370\"\u003E[37, Section 9.11]\u003C\u002Fa\u003E. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented. In particular, we include a categorical interpretation of the “Koszulity implies K(π,1)\u003Cmath\u003E\u003Cmo\u003E\u003Cmo\u003E” claim, discuss the differences between two versions of Massey operations, and apply the derived nonhomogeneous Koszul duality theory in order to deduce the main theorem. In the end we demonstrate a counterexample providing a negative answer to a question of Hopkins and Wickelgren about formality of the cochain DG-algebras of absolute Galois groups, thus showing that quasi-formality cannot be strengthened to formality in the title assertion.\u003C\u002Fp\u003E\n"},"priorityTarget":[{"id":"66508910","title":"математика","en_title":"mathematics"}],"researchTarget":[],"keywords":[{"id":"102132162","title":"formality"},{"id":"128903098","title":"Galois cohomology"},{"id":"206613458","title":"Nonhomogeneous quadratic relations"},{"id":"206613462","title":"Conilpotent coalgebras"},{"id":"206613466","title":"Koszul duality"},{"id":"206613470","title":"t-Structures of derived type"},{"id":"206613474","title":"Massey products"},{"id":"206613478","title":"Quasi-formality"},{"id":"206613484","title":"Noncommutative homotopy theory"},{"id":"206613488","title":"Galois groups"}],"language":{"id":"20592","title":{"ru":"английский","en":"English"},"name":"en"},"related":[{"id":"1184189406","title":"Произведения Масси и соотношения в когомологиях алгебр Стинрода","createdAt":"2026-07-28T15:48:37.610Z","authorsByType":{"author":[{"id":"768859984","href":"\u002Forg\u002Fpersons\u002F768859984","title":{"ru":"Попеленский Ф. Ю.","en":"Popelensky T."},"altName":"Попеленский Ф. Ю.","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"\u003Cp\u003EВ недавней работе В. М. Бухштабера и автора была введена новая структура в когомологиях алгебр Хопфа в терминах спектральной последовательности Бухштабера (Bss). В классической алгебре Стинрода A2 имеется важная подалгебра Хопфа A(1), когомологии которой давно известны. В настоящей работе обсуждаемая структура на этих когомологиях полностью вычислена.\u003Cbr\u002F\u003E\nВ рамках демонстрации методов Bss решена обратная задача: получено новое явное вычисление s-мерных когомологий алгебры A(1) для s ⩽ 4. Методами Bss также получены результаты о произведениях Масси и\u003Cbr\u002F\u003E\nсоотношениях в когомологиях алгебр Стинрода Ap, p ⩾ 2.\u003C\u002Fp\u003E\n","en":"\u003Cp\u003EIn a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.\u003Cbr\u002F\u003E\nAs part of a demonstration of the methods of Bss, we solve the inverse problem and present a new explicit calculation of the s-dimensional cohomology of the algebra A(1) for s ⩽ 4.\u003Cbr\u002F\u003E\nWe also use the methods of Bss to obtain results on the Massey products and relations in the cohomology of the Steenrod algebras Ap, p ⩾ 2.\u003C\u002Fp\u003E\n"},"description":{"short":{"publ":"Математический сборник 2026 Т. 217 № 2 С. 108-153","en":"Sbornik Mathematics 2026 Vol. 217 No. 2 P. 108-153","ru":"Математический сборник 2026 Т. 217 № 2 С. 108-153"},"main":"Попеленский Ф. Ю. Произведения Масси и соотношения в когомологиях алгебр Стинрода \u002F\u002F Математический сборник. 2026. Т. 217. № 2. С. 108-153."}},{"id":"1181654310","title":"New bound on S1\times S2-setting Bell locality of a nonseparable Werner state","createdAt":"2026-07-21T06:25:29.749Z","authorsByType":{"author":[{"id":"191485331","href":"\u002Forg\u002Fpersons\u002F191485331","title":{"ru":"Лубенец Е. Р.","en":"Loubenets E. R."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2\geq1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a dimension d\leqmin {S1,S2} to satisfy all Bell inequalities under every S1\timesS2-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous -- that is, to be S1\timesS2-setting -setting Bell local, for short. For a variety of S1,S2\geq1 values, this new general locality condition is beyond Werner’s and Barrett’s locality conditions for a nonseparable Werner state. We also prove explicitly in the operator terms the optimization result by Terhal et. el. [Phys. Rev. Lett. 90, 157903 (2003)] via semi-programming that every nonseparable Werner state with a dimension d> min {S1,S2} is S1\timesS2-setting Bell local. The new results of the present article are important both for Bell nonlocality theory and for quantum applications based on Bell nonlocality.\n"},"description":{"short":{"publ":"\u002F Series arxiv.org \"quant-ph\". 2026. No. 2607.18050.","en":"\u002F Series arxiv.org \"quant-ph\". 2026. No. 2607.18050.","ru":"\u002F Серия arxiv.org \"quant-ph\". 2026. № 2607.18050."},"main":"Loubenets E. R. New bound on S1\times S2-setting Bell locality of a nonseparable Werner state \u002F Series arxiv.org \"quant-ph\". 2026. No. 2607.18050."}},{"id":"1180109721","title":"On functional equations for Chow polylogarithms","createdAt":"2026-07-16T09:35:09.151Z","authorsByType":{"author":[{"id":"65799783","href":"\u002Fstaff\u002Fvbolbachan","title":{"ru":"Болбачан В. С.","en":"Bolbachan V."},"altName":"","otherName":""}]},"year":2024,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"Полилогарифмы Чжоу — это специальные функции, возникающие при явном описании отображения регулятора Бейлинсона. Наиболее интересное функциональное уравнение для этой функции отражает тот факт, что она обращается в нуль на границе в комплексе циклов Блоха. Мы показываем, что это функциональное уравнение формально вытекает из более простых свойств: кососимметричности, функториальности и мультипликативности. Для доказательства этого мы рассматриваем аналог комплекса циклов Блоха и устанавливаем для него аналог гипотезы Бейлинсона — Суле об обращении в нуль. А. Гончаров определил группу функциональных уравнений для классических полилогарифмов. Мы показываем, что любое такое функциональное уравнение формально следует из сформулированных выше функциональных уравнений для полилогарифмов Чжоу.\n","en":" \n\nChow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.\nTo prove this, we study some analogue of Bloch's cycle complex and establish for this complex an analogue Beilinson-Soule vanishing conjecture.\nA. Goncharov defined a group of functional equations for classical polylogarithms. We show that any such functional equation formally follows from functional equations for Chow polylogarithms stated above.\n"},"description":{"short":{"publ":"\u002F Series math \"arxiv.org\". 2024.","en":"\u002F Series math \"arxiv.org\". 2024.","ru":"\u002F Серия math \"arxiv.org\". 2024."},"main":"Bolbachan V. On functional equations for Chow polylogarithms \u002F Series math \"arxiv.org\". 2024."}},{"id":"1180107418","title":"On Goncharov’s conjecture in next to Milnor degree","createdAt":"2026-07-16T09:24:19.389Z","authorsByType":{"author":[{"id":"65799783","href":"\u002Fstaff\u002Fvbolbachan","title":{"ru":"Болбачан В. С.","en":"Bolbachan V."},"altName":"","otherName":""}]},"year":2024,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"Пусть K поле характеристики ноль. Мы доказываем что его когомологии в степени m-1 и весе m рационально изоморфны когомологиям полилогарифмического комплекса в соответствующей степени. Это дает частичное расширение теоремы Суслина, описывающую неразложимую K теорию K_3 для поля.\n","en":"Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m-1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field.\n"},"description":{"short":{"publ":"\u002F Series math \"arxiv.org\". 2024.","en":"\u002F Series math \"arxiv.org\". 2024.","ru":"\u002F Серия math \"arxiv.org\". 2024."},"main":"Bolbachan V. On Goncharov’s conjecture in next to Milnor degree \u002F Series math \"arxiv.org\". 2024."}},{"id":"1177496035","title":"Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond","createdAt":"2026-07-08T21:18:29.956Z","authorsByType":{"author":[{"id":"93419930","href":"\u002Forg\u002Fpersons\u002F93419930","title":{"ru":"Панов В. А.","en":"Panov V."},"altName":"","otherName":""},{"id":"870180136","href":"\u002Forg\u002Fpersons\u002F870180136","title":{"ru":"Рябченко А. П.","en":"Ryabchenko A."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class of rational-infinitely divisible distributions. We propose an estimation framework based on band-limited kernels, which are the functions characterized by compactly supported Fourier transform. Under mild assumptions, the proposed estimators are theoretically shown to achieve polynomial (and in some cases even almost parametric) convergence rates. Finally, we demonstrate the numerical performance of the algorithm on simulated examples.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"stat.ME\". 2026. No. 2607.05048.","en":"\u002F Series arXiv \"stat.ME\". 2026. No. 2607.05048.","ru":"\u002F Серия arXiv \"stat.ME\". 2026. № 2607.05048."},"main":"Panov V., Ryabchenko A. Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond \u002F Series arXiv \"stat.ME\". 2026. No. 2607.05048."}},{"id":"1168392208","title":"Strong Approximations for Markov Chains Weakly Converging to Diffusions","createdAt":"2026-06-11T14:02:44.934Z","authorsByType":{"author":[{"id":"22565341","href":"\u002Forg\u002Fpersons\u002F22565341","title":{"ru":"Конаков В. Д.","en":"Konakov V."},"altName":"","otherName":""},{"id":"510331770","href":"\u002Forg\u002Fpersons\u002F510331770","title":{"ru":"Кучер Д. А.","en":"Kucher D."},"altName":"","otherName":""},{"id":"1168403979","href":null,"title":{"ru":"Enno M.","en":"Mammen E."},"altName":"Mammen E.","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability of their exact pathwise coincidence on discrete time grids. Moreover, we construct such probability space that the probability of a large deviation of the interpolated Markov chain from the continuous diffusion trajectory is small on the entire time interval.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026. No. 2606.11142v1.","en":"\u002F Series arXiv \"math\". 2026. No. 2606.11142v1.","ru":"\u002F Серия arXiv \"math\". 2026. № 2606.11142v1."},"main":"Konakov V., Kucher D., Mammen E. Strong Approximations for Markov Chains Weakly Converging to Diffusions \u002F Series arXiv \"math\". 2026. No. 2606.11142v1."}},{"id":"1159023519","title":"Bifurcations and Structural Stability of Generic PC-HC Families","createdAt":"2026-05-14T20:14:13.617Z","authorsByType":{"author":[{"id":"225531552","href":"\u002Forg\u002Fpersons\u002F225531552","title":{"ru":"Доровский А. А.","en":"Dorovskiy A."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. Furthermore, bifurcation diagrams for the considered class of families are constructed.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026.","en":"\u002F Series arXiv \"math\". 2026.","ru":"\u002F Серия arXiv \"math\". 2026."},"main":"Dorovskiy A. Bifurcations and Structural Stability of Generic PC-HC Families \u002F Series arXiv \"math\". 2026."}},{"id":"1154890848","title":"On the minimum number of maximal distance-k independent sets in trees","createdAt":"2026-05-01T16:34:26.193Z","authorsByType":{"author":[{"id":"234904499","href":"\u002Fstaff\u002Fdmital","title":{"ru":"Талецкий Д. С.","en":"Taletskii D."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"A vertex subset of a graph is called a \\textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \\geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \\leq k + 1$, and $n - \\bigg\\lfloor \\frac{n - (k \\bmod 2)}{\\lfloor k\u002F2 \\rfloor + 1} \\bigg\\rfloor + 1$ otherwise. We also completely describe the class of trees attaining this bound and determine the growth rate of the number of such $n$-vertex trees for a fixed $k \\geq 1$. If $k$ is odd and $(k+1)\u002F2$ does not divide $n-1$, then the number of non-isomorphic $n$-vertex trees with the minimum possible number of maximal distance-$k$ independent sets grows linearly with~$n$. Otherwise, it is bounded above by the number of unlabeled $k^2$-vertex trees.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026.","en":"\u002F Series arXiv \"math\". 2026.","ru":"\u002F Серия arXiv \"math\". 2026."},"main":"Taletskii D. On the minimum number of maximal distance-k independent sets in trees \u002F Series arXiv \"math\". 2026."}},{"id":"1154452444","title":"On Arithmetic Mirror Symmetry for smooth Fano fourfolds","createdAt":"2026-04-30T08:10:07.484Z","authorsByType":{"author":[{"id":"305107770","href":"\u002Forg\u002Fpersons\u002F305107770","title":{"ru":"Овчаренко М. А.","en":"Ovcharenko M."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, or are quiver flag zero loci. We discuss implications to Arithmetic Mirror Symmetry conjecture, a Hodge-theoretic approach to the study of Apéry constants of Fano varieties proposed by Golyshev--Kerr--Sasaki. Using the partial case of Arithmetic Mirror Symmetry conjecture proved by Kerr, we construct two examples of a Mirror Symmetry correspondence between specific algebraic classes.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026.","en":"\u002F Series arXiv \"math\". 2026.","ru":"\u002F Серия arXiv \"math\". 2026."},"main":"Ovcharenko M. On Arithmetic Mirror Symmetry for smooth Fano fourfolds \u002F Series arXiv \"math\". 2026."}},{"id":"1150339242","title":"On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization","createdAt":"2026-04-18T15:03:02.788Z","authorsByType":{"author":[{"id":"22740475","href":"\u002Fstaff\u002Fazlotnik","title":{"ru":"Злотник А. А.","en":"Zlotnik A."},"altName":"Zlotnik Alexander","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\\eta,u,\\theta)$, in a norm slightly stronger than $L^{2,\\infty}(Q)\\times L^2(Q)\\times L^2(Q)$, on the initial data $(\\eta^0,u^0,e^0)$ in a norm of $L^2(\\Omega)\\times H^{-1}(\\Omega)\\times H^{-1}(\\Omega)$--type and also on the free terms in all the equations in some dual norms. Here $\\eta$, $u$ and $\\theta$ are the specific volume, velocity and absolute temperature as well as $\\eta^0$, $u^0$ and $e^0$ are the initial specific volume, velocity and specific total energy, and $Q=\\Omega\\times (0,T)$. We also apply this result to the case of discontinuous rapidly oscillating, with the period $\\ve$, initial data and free terms and derive an estimate $O(\\ve)$ for the difference between the solutions to the Navier-Stokes equations and their Bakhvalov-Eglit two-scale homogenized version with averaged data.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026. No. 2602.03481v1.","en":"\u002F Series arXiv \"math\". 2026. No. 2602.03481v1.","ru":"\u002F Серия arXiv \"math\". 2026. № 2602.03481v1."},"main":"Zlotnik A. On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization \u002F Series arXiv \"math\". 2026. No. 2602.03481v1."}},{"id":"1144324258","title":"On the dimension of the space of static potentials on three-manifolds","createdAt":"2026-04-03T06:25:30.903Z","authorsByType":{"author":[{"id":"101534432","href":"\u002Forg\u002Fpersons\u002F101534432","title":{"ru":"Медведев В. О.","en":"Medvedev V."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a compact static manifold with boundary admits a static potential whose zero set is disjoint from the boundary, then the space of static potentials is necessarily one-dimensional. These results rely on a careful analysis of the relative positions of the zero sets of linearly independent static potentials - a technique originally introduced by Miao and Tam.\n","en":"We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a compact static manifold with boundary admits a static potential whose zero set is disjoint from the boundary, then the space of static potentials is necessarily one-dimensional. These results rely on a careful analysis of the relative positions of the zero sets of linearly independent static potentials - a technique originally introduced by Miao and Tam.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2026.","en":"\u002F Series arXiv \"math\". 2026.","ru":"\u002F Серия arXiv \"math\". 2026."},"main":"Medvedev V. On the dimension of the space of static potentials on three-manifolds \u002F Series arXiv \"math\". 2026."}},{"id":"1144059053","title":"Using predefined vector systems to speed up neural network multimillion class classification","createdAt":"2026-04-02T08:06:09.019Z","authorsByType":{"author":[{"id":"1144059064","href":null,"title":{"ru":"Nikita G.","en":"Gabdullin N."},"altName":"Gabdullin N.","otherName":""},{"id":"1038923829","href":"\u002Fstaff\u002Fandrosov","title":{"ru":"Андросов И. А.","en":"Androsov I."},"altName":"","otherName":""}]},"year":2026,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can be significantly reduced. This is achieved by associating label prediction with the O(1) complexity closest cluster center search in a vector system used as target for latent space configuration (LSC). The proposed method only requires finding indexes of several largest and lowest values in the embedding vector making it extremely computationally efficient. We show that the proposed method does not change NN training accuracy computational results. We also measure the time required by different computational stages of NN inference and label prediction on multiple datasets. The experiments show that the proposed method allows to achieve up to 11.6 times overall acceleration over conventional methods. Furthermore, the proposed method has unique properties which allow to predict the existence of new classes.\n"},"description":{"short":{"publ":"\u002F Series Computer Science \"arxiv.org\". 2026.","en":"\u002F Series Computer Science \"arxiv.org\". 2026.","ru":"\u002F Серия Computer Science \"arxiv.org\". 2026."},"main":"Gabdullin N., Androsov I. Using predefined vector systems to speed up neural network multimillion class classification \u002F Series Computer Science \"arxiv.org\". 2026."}},{"id":"1128282882","title":"Homogeneous maximizers of the Blaschke-Santalo-type functionals","createdAt":"2026-02-13T14:49:59.105Z","authorsByType":{"author":[{"id":"23597497","href":"\u002Forg\u002Fpersons\u002F23597497","title":{"ru":"Колесников А. В.","en":"Kolesnikov A."},"altName":"","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.\nWe also discuss links to the multimagrinal optimal transportation problem and the related sharp transportation-information inequalities.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2025.","en":"\u002F Series arXiv \"math\". 2025.","ru":"\u002F Серия arXiv \"math\". 2025."},"main":"Kolesnikov A. Homogeneous maximizers of the Blaschke-Santalo-type functionals \u002F Series arXiv \"math\". 2025."}},{"id":"1119268025","title":"Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection","createdAt":"2026-01-15T15:39:58.509Z","authorsByType":{"author":[{"id":"305123525","href":"\u002Fstaff\u002Fksorokin","title":{"ru":"Сорокин К. С.","en":"Sorokin K."},"altName":"","otherName":""},{"id":"309254254","href":null,"title":{"ru":"Бекетов М. Е.","en":"Beketov M."},"altName":"","otherName":""},{"id":"1119268150","href":null,"title":{"ru":"Арсений О.","en":"Онучин А."},"altName":"Онучин А.","otherName":""},{"id":"1119268152","href":null,"title":{"ru":"Любовь Т.","en":"Тупикина Л."},"altName":"Тупикина Л.","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"Обнаружение сообществ в сложных сетях — фундаментальная проблема, открытая для новых подходов в различных научных областях. Мы представляем новый метод обнаружения сообществ, основанный на потоке Риччи на графах. Наша техника итеративно обновляет веса ребер (их метрические длины) в соответствии с их (комбинаторной) версией кривизны Риччи Фостера, вычисленной на основе эффективного расстояния сопротивления между узлами. Известно, что последнее вычисление выполняется путем псевдоинвертирования матрицы Лапласа графа. При этом наш подход является альтернативой подходу, основанному на геометрическом потоке Олливье-Риччи для обнаружения сообществ на графах, значительно превосходя его по времени вычислений. В предлагаемом нами методе итерации потока Фостера-Риччи, которые выделяют области сети с различной кривизной, сопровождаются эвристикой разделения с помощью модели гауссовой смеси (GMM). Это позволяет классифицировать ребра на «сильные» (внутрисообщественные) и «слабые» (межсообщественные) группы, после чего происходит систематическое отсечение первых для изоляции сообществ. Мы провели сравнительный анализ нашего алгоритма на синтетических сетях, сгенерированных на основе стохастической блочной модели (SBM), оценивая производительность с помощью скорректированного индекса ARI. Наши результаты показывают, что предложенная структура надежно восстанавливает структуру сообществ, созданных на основе SBM, подтверждая, что поток Риччи-Фостера с кластеризацией GMM является принципиально эффективным и вычислительно действенным новым инструментом для анализа сетей, протестированным в сравнении с альтернативным потоком Риччи-Оливье в сочетании со спектральной кластеризацией.\n","en":"Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the nodes. The latter computation is known to be done by pseudo-inverting the graph Laplacian matrix. At that, our approach is alternative to one based on Ollivier-Ricci geometric flow for community detection on graphs, significantly outperforming it in terms of computation time. In our proposed method, iterations of Foster-Ricci flow that highlight network regions of different curvature -- are followed by a Gaussian Mixture Model (GMM) separation heuristic. That allows to classify edges into ''strong'' (intra-community) and ''weak'' (inter-community) groups, followed by a systematic pruning of the former to isolate communities. We benchmark our algorithm on synthetic networks generated from the Stochastic Block Model (SBM), evaluating performance with the Adjusted Rand Index (ARI). Our results demonstrate that proposed framework robustly recovers the planted community structure of SBM-s, establishing Ricci-Foster Flow with GMM-clustering as a principled and computationally effective new tool for network analysis, tested against alternative Ricci-Ollivier flow coupled with spectral clustering.\n"},"description":{"short":{"publ":"\u002F arxiv.org. Серия cs.SI \"Social and Information Networks \". 2025.","en":"\u002F arxiv.org. Series cs.SI \"Social and Information Networks \". 2025.","ru":"\u002F arxiv.org. Серия cs.SI \"Social and Information Networks \". 2025."},"main":"Сорокин К. С., Бекетов М. Е., Арсений О. и др. Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection \u002F arxiv.org. Серия cs.SI \"Social and Information Networks \". 2025."}},{"id":"1113673246","title":"On finding formal power-logarithmic expansions of solutions to q-difference equations","createdAt":"2025-12-25T03:51:36.916Z","authorsByType":{"author":[{"id":"305068394","href":"\u002Forg\u002Fpersons\u002F305068394","title":{"ru":"Гаянов Н. В.","en":"Gaianov N."},"altName":"","otherName":""},{"id":"47634692","href":"\u002Forg\u002Fpersons\u002F47634692","title":{"ru":"Парусникова А. В.","en":"Parusnikova A."},"altName":"","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"Рассматривается алгебраическое q-разностное уравнение. Предлагается достаточное условие существования формального степенно- логарифмического разложения решения такого уравнения в окрест- ности нуля. Приводится пример применения этого достаточного условия для построения формального разложения решения неко- торого q-разностного аналога пятого уравнения Пенлеве при конкретных значениях параметров уравнения; рассматриваются два различных значения числа q, приводящие к качественно разным формальным асимптотическим разложениям решений.\n","en":"An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation for specific values of the equation parameters is given; two different values of the number q are considered, leading to qualitatively different formal asymptotic expansions of the solutions of the fifth Painlevé equation.\n"},"description":{"short":{"publ":"\u002F Cornell University. Серия math \"arxiv.org\". 2025.","en":"\u002F Cornell University. Series math \"arxiv.org\". 2025.","ru":"\u002F Cornell University. Серия math \"arxiv.org\". 2025."},"main":"Гаянов Н. В., Парусникова А. В. On finding formal power-logarithmic expansions of solutions to q-difference equations \u002F Cornell University. Серия math \"arxiv.org\". 2025."}},{"id":"1111292211","title":"Ideal of the variety of flexes of plane cubics","createdAt":"2025-12-16T14:09:57.077Z","authorsByType":{"author":[{"id":"47634458","href":"\u002Forg\u002Fpersons\u002F47634458","title":{"ru":"Попов В. Л.","en":"Popov V."},"altName":"","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"We prove that the variety of flexes of algebraic curves\nof degree 3 in the projective plane is an ideal theoretic complete\nintersection in the product of a two-dimensional and a nine-dimen-\nsional projective spaces.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2025. No. 2502.01539.","en":"\u002F Series arXiv \"math\". 2025. No. 2502.01539.","ru":"\u002F Серия arXiv \"math\". 2025. № 2502.01539."},"main":"Popov V. Ideal of the variety of flexes of plane cubics \u002F Series arXiv \"math\". 2025. No. 2502.01539."}},{"id":"1108157029","title":"Random walks on rank one symmetric spaces of noncompact type","createdAt":"2025-12-05T14:18:23.607Z","authorsByType":{"author":[{"id":"969293123","href":"\u002Forg\u002Fpersons\u002F969293123","title":{"ru":"Гнетов Ф. А.","en":"Gnetov F."},"altName":"","otherName":""},{"id":"22565341","href":"\u002Forg\u002Fpersons\u002F22565341","title":{"ru":"Конаков В. Д.","en":"Konakov V."},"altName":"","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural\nrandom walk on a symmetric space M of non-compact type and rank one. This class of spaces, which\nincludes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes\nthe real hyperbolic space Hn. Our approach introduces a unified algebraic framework that generalizes\nthe M¨obius addition, previously used for the constant curvature case, to define the random walk via a\nnon-Euclidean summation of variables. We demonstrate that the renormalized walk converges to the\nheat kernel associated with the Laplace-Beltrami operator on M, which plays the role of the limiting\nnormal law. The proofs leverage the harmonic analysis of spherical functions on symmetric spaces. To\nthe best of our knowledge, these results are new in the context of rank one symmetric spaces.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2025. No. 2512.04667.","en":"\u002F Series arXiv \"math\". 2025. No. 2512.04667.","ru":"\u002F Серия arXiv \"math\". 2025. № 2512.04667."},"main":"Gnetov F., Konakov V. Random walks on rank one symmetric spaces of noncompact type \u002F Series arXiv \"math\". 2025. No. 2512.04667."}},{"id":"1107827627","title":"Cascades of Lorenz attractors in the Shimizu-Morioka model","createdAt":"2025-12-04T16:12:24.983Z","authorsByType":{"author":[{"id":"143572326","href":"\u002Forg\u002Fpersons\u002F143572326","title":{"ru":"Казаков А. О.","en":"Kazakov A."},"altName":"","otherName":""},{"id":"305090592","href":"\u002Forg\u002Fpersons\u002F305090592","title":{"ru":"Корякин В. А.","en":"Koryakin V."},"altName":"","otherName":""},{"id":"307981721","href":"\u002Forg\u002Fpersons\u002F307981721","title":{"ru":"Сафонов К. А.","en":"Safonov K."},"altName":"","otherName":""},{"id":"1107828019","href":null,"title":{"ru":"Andrei S.","en":"Shilnikov A."},"altName":"Shilnikov A.","otherName":""}]},"year":2025,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. As in the classical Lorenz system, a part of the boundary is associated with the curve $l_{A=0}$, where the first tangency between some Lyapunov subspaces occurs along orbits of the attractor. However, in the Lorenz system, the curve $l_{A=0}$ forms the exact boundary of the Lorenz attractor existence region. Beyond this curve, the attractor is not robustly chaotic, although it may be indistinguishable from the Lorenz attractor in simple numerical experiments. In the Shimizu-Morioka model, the curve $l_{A=0}$ is divided into two parts. The Lorenz attractor existence region adjoins $l_{A=0}$ along the first part of this curve, as in the Lorenz system. Near the second part, as we show, the region of the existence of the Lorenz attractor is fractal. We describe two infinite cascades of disjoint subregions with the Lorenz attractor. One cascade occurs along the curve $l_{A=0}$, another -- in the transversal direction. We show that along the cascades, the Lorenz attractor undergoes ``doubling bifurcations'', leading to a complication of its topological structure.\n"},"description":{"short":{"publ":"\u002F Series arXiv \"math\". 2025.","en":"\u002F Series arXiv \"math\". 2025.","ru":"\u002F Серия arXiv \"math\". 2025."},"main":"Kazakov A., Koryakin V., Safonov K. et al. Cascades of Lorenz attractors in the Shimizu-Morioka model \u002F Series arXiv \"math\". 2025."}},{"id":"894036201","title":"On cubic polynomials with the cyclic Galois group","createdAt":"2024-02-05T10:39:26.290Z","authorsByType":{"author":[{"id":"47634461","href":"\u002Forg\u002Fpersons\u002F47634461","title":{"ru":"Кочетков Ю. Ю.","en":"Kochetkov Y."},"altName":"","otherName":""}]},"year":2024,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"A cubic Galois polynomial is a cubic polynomial with rational coefficients that defines a cubic Galois field. Its\ndiscriminant is a full square and its roots $x_1,x_2,x_3$ (enumerated in some order) are real. There exists (and only one) quadratic polynomial $q$ with rational coefficients such that $q(x_1)=x_2, q(x_2)=x_3, q(x_3)=x_1$. The polynomial $r=q(q) \\text{ mod } p$ cyclically permutes roots of $p$ in the opposite order: $r(x_1)=x_3, r(x_3)=x_2, r(x_2)=x_1$. We prove that there exist a unique Galois polynomial $p_1$ and a unique Galois polynomial $p_2$ such that the polynomial $q$ cyclically permutes roots of $p_1$ and the polynomial $r$ do the same with roots of $p_2$. Polynomials $p$ and $p_1$ (and also $p$ and $p_2$) will be called \\emph{coupled}. Two polynomials are \\emph{linear equivalent}, if one of them is obtained from another by a linear change of variable. By $C(p)$ we denote the class of polynomials, linear equivalent to $p$. The coupling realizes a bijection between classes $C(p)$ and $C(p_1)$ (and between classes $C(p)$ and $C(p_2)$). Classes $C(p)$ and $C(p_1)$ (and classes $C(p)$ and\n$C(p_2)$) will be called \\emph{adjacent}. We consider a graph: its vertices --- are classes of the linear equivalency and two vertices are connected by an edge, if the corresponded classes are adjacent. Connected components of this graph will be called \\emph{superclasses}. In this work we give a description of superclasses.\n"},"description":{"short":{"publ":"\u002F Series arXiv.org e-print archive \"arXiv.math\". 2024. No. 2401.11208.","en":"\u002F Series arXiv.org e-print archive \"arXiv.math\". 2024. No. 2401.11208.","ru":"\u002F Серия arXiv.org e-print archive \"arXiv.math\". 2024. № 2401.11208."},"main":"Kochetkov Y. On cubic polynomials with the cyclic Galois group \u002F Series arXiv.org e-print archive \"arXiv.math\". 2024. No. 2401.11208."}},{"id":"809248535","title":"Koszul algebras and Donaldson-Thomas invariants","createdAt":"2023-01-20T18:13:52.017Z","authorsByType":{"author":[{"id":"813274386","href":null,"title":{"ru":"Vladimir D.","en":"Dotsenko V."},"altName":"Dotsenko V.","otherName":""},{"id":"14010827","href":"\u002Forg\u002Fpersons\u002F14010827","title":{"ru":"Фейгин Е. Б.","en":"Feigin E."},"altName":"","otherName":""},{"id":"813274390","href":null,"title":{"ru":"Markus R.","en":"Reineke M."},"altName":"Reineke M.","otherName":""}]},"year":2022,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"\u003Cp\u003EWe propose a new method for computing motivic Donaldson-Thomas invariants of a symmetric quiver which relies on Koszul duality between supercommutative algebras and Lie superalgebras and completely bypasses cohomological Hall algebras. Specifically, we define, for a given symmetric quiver \u003Cem\u003EQ\u003C\u002Fem\u003E, a supercommutative quadratic algebra A_Q, and study the Lie superalgebra g_Q that corresponds to A_Q under Koszul duality. We introduce an action of the first Weyl algebra on g_Q and prove that the motivic Donaldson-Thomas invariants of \u003Cem\u003EQ\u003C\u002Fem\u003E may be computed via the Poincaré series of the kernel of the operator \partial\u003Cem\u003Et\u003C\u002Fem\u003E. This gives a new proof of positivity for motivic Donaldson-Thomas invariants. Along the way, we prove that the algebra A_Q is numerically Koszul for every symmetric quiver \u003Cem\u003EQ\u003C\u002Fem\u003E and conjecture that it is in fact Koszul; we show that this conjecture holds for a certain class of quivers.\u003C\u002Fp\u003E\n"},"description":{"short":{"publ":"Letters in Mathematical Physics 2022 Vol. 112 No. 5 Article 106","en":"Letters in Mathematical Physics 2022 Vol. 112 No. 5 Article 106","ru":"Letters in Mathematical Physics 2022 Т. 112 № 5 Статья 106"},"main":"Dotsenko V., Feigin E., Reineke M. Koszul algebras and Donaldson-Thomas invariants \u002F\u002F Letters in Mathematical Physics. 2022. Vol. 112. No. 5. Article 106."}},{"id":"764630270","title":"Koszul duality for simplicial restricted Lie algebras","createdAt":"2022-09-12T15:59:23.078Z","authorsByType":{"author":[{"id":"65820943","href":null,"title":{"ru":"Коновалов Н. С.","en":null},"altName":"Nikolay Konovalov","otherName":""}]},"year":2022,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"Let $\\mathsf{s}_0\\mathsf{Lie}^r$ be the category of $0$-reduced simplicial restricted Lie algebras over a fixed perfect field of positive characteristic $p$. We prove that there is a full subcategory $\\mathrm{Ho}(\\mathsf{s}_0\\mathsf{Lie}^r_{\\xi})$ of the homotopy category $\\mathrm{Ho}(\\mathsf{s}_0\\mathsf{Lie}^r)$ and an equivalence $\\mathrm{Ho}(\\mathsf{s}_0\\mathsf{Lie}^r_{\\xi})\\simeq\\mathrm{Ho}(\\mathsf{s}_1\\mathsf{CoAlg}^{tr})$. Here $\\mathsf{s}_1\\mathsf{CoAlg}^{tr}$ is the category of $1$-reduced simplicial truncated coalgebras; informally, a coaugmented cocommutative coalgebra $C$ is truncated if $x^p=0$ for any $x$ from the augmentation ideal of the dual algebra $C^*$. Moreover, we provide a sufficient and necessary condition in terms of the homotopy groups $\\pi_*(L_\\bullet)$ for $L_\\bullet \\in \\mathrm{Ho}(\\mathsf{s}_0\\mathsf{Lie}^r)$ to lie in the full subcategory $\\mathrm{Ho}(\\mathsf{s}_0\\mathsf{Lie}^r_{\\xi})$.\nAs an application of the equivalence above, we construct and examine an analog of the unstable Adams spectral sequence of A. K. Bousfield and D. Kan in the category $\\mathsf{sLie}^r$. We use this spectral sequence to recompute the homotopy groups of a free simplicial restricted Lie algebra.\n"},"description":{"short":{"publ":"\u002F Series \"Working papers by Cornell University\". 2022. No. 2209.03312.","en":"\u002F Series \"Working papers by Cornell University\". 2022. No. 2209.03312.","ru":"\u002F Серия \"Working papers by Cornell University\". 2022. № 2209.03312."},"main":"Коновалов Н. С. Koszul duality for simplicial restricted Lie algebras \u002F Series \"Working papers by Cornell University\". 2022. No. 2209.03312."}},{"id":"759628188","title":"Минимально неголодовы кольца граней и произведения Масси","createdAt":"2022-09-08T19:13:53.310Z","authorsByType":{"author":[{"id":"305969388","href":null,"title":{"ru":"Лимонченко И. Ю.","en":"Limonchenko I."},"altName":"","otherName":""},{"id":"14061554","href":"\u002Forg\u002Fpersons\u002F14061554","title":{"ru":"Панов Т. Е.","en":"Panov T."},"altName":"","otherName":""}]},"year":2022,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":"\u003Cp\u003EВ статье получен критерий голодовости кольца граней k[K] симплициального комплекса K над полем k. Подобный критерий был предложен в статье Ву-Грбич-Панова-Терио, но одно из утверждений в нем опиралось на основной результат работы Берглунда-Йолленбека, контрпример к которому найден в статье Каттена. Наше доказательство устраняет этот пробел. Мы также строим пример минимально неголодова комплекса K такого, что в когомологиях его момент-угол-комплекса Z_K умножение тривиально, но имеется нетривиальное тройное произведение Масси.\u003C\u002Fp\u003E\n","en":"\u003Cp\u003EWe give a correct statement and a complete proof of the criterion obtained in a paper of Grbic-Panov-Theriault-Wu for the face rin k[K] of a simplicial complex K to be Golod over a field k. (The original argument depended on the main result of Berglund and Joellenbeck, which was shown to be false by Katthaen.) We also construct an example of a minimally non-Golod complex K such that the cohomology of the corresponding moment-angle complex Z_K has trivial cup product and a non-trivial triple Massey product.\u003C\u002Fp\u003E\n"},"description":{"short":{"publ":"Успехи математических наук 2022 Т. 77 № 4 С. 203-204","en":"Russian Mathematical Surveys 2022 Vol. 77 No. 4 P. 203-204","ru":"Успехи математических наук 2022 Т. 77 № 4 С. 203-204"},"main":"Лимонченко И. Ю., Панов Т. Е. Минимально неголодовы кольца граней и произведения Масси \u002F\u002F Успехи математических наук. 2022. Т. 77. № 4. С. 203-204."}},{"id":"524053861","title":"Massey Products in the Cohomology of the Moment-Angle Manifolds Corresponding to Pogorelov Polytopes","createdAt":"2021-10-31T09:17:51.999Z","authorsByType":{"author":[{"id":"523778545","href":null,"title":{"ru":"Журавлева Е. Г.","en":"Zhuravleva E."},"altName":"E. G. Zhuravleva","otherName":""}]},"year":2019,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":"\u003Cp\u003ENontrivial Massey products in the cohomology of the moment-angle manifolds corresponding to polytopes in the Pogorelov class are constructed. This class includes the dodecahedron and all fullerenes, i.e., simple 3-polytopes with only 5- and 6-gonal faces. The existence of nontrivial Massey products implies that the spaces under consideration are not formal in the sense of rational homotopy theory.\u003C\u002Fp\u003E\n"},"description":{"short":{"publ":"Mathematical notes 2019 Vol. 105 No. 4 P. 519-527","en":"Mathematical notes 2019 Vol. 105 No. 4 P. 519-527","ru":"Математические заметки 2019 Т. 105 № 4 С. 519-527"},"main":"Zhuravleva E. Massey Products in the Cohomology of the Moment-Angle Manifolds Corresponding to Pogorelov Polytopes \u002F\u002F Mathematical notes. 2019. Vol. 105. No. 4. P. 519-527."}},{"id":"516605782","title":"Higher order Massey products and applications","createdAt":"2021-10-12T21:40:49.356Z","authorsByType":{"author":[{"id":"305969388","href":null,"title":{"ru":"Лимонченко И. Ю.","en":"Limonchenko I."},"altName":"","otherName":""},{"id":"523096319","href":null,"title":{"ru":"Dmitry M.","en":"Millionshchikov D."},"altName":"Millionshchikov D.","otherName":""}]},"year":2021,"publisher":{"title":{"ru":null,"en":null}},"annotation":{"ru":null,"en":null},"description":{"short":{"publ":", in: Contemporary Mathematics, Topology, Geometry, and Dynamics V.A.Rokhlin-MemorialVol. 772.: United States of America: American Mathematical Society, 2021. P. 209-240.","en":", in : Contemporary Mathematics, Topology, Geometry, and Dynamics V.A.Rokhlin-Memorial. Vol. 772.: United States of America: American Mathematical Society, 2021. P. 209-240.","ru":"В кн. : Contemporary Mathematics, Topology, Geometry, and Dynamics V.A.Rokhlin-Memorial. Т. 772.: Соединенные Штаты Америки: American Mathematical Society, 2021. С. 209-240."},"main":"Limonchenko I., Millionshchikov D. , in : Contemporary Mathematics, Topology, Geometry, and Dynamics V.A.Rokhlin-Memorial. Vol. 772.: United States of America: American Mathematical Society, 2021. P. 209-240."}}],"metaTegs":[{"id":"twitter_card","name":"twitter:card","content":"summary"},{"id":"og:title","property":"og:title","content":"Koszulity of cohomology = K(π,1)-ness + quasi-formality"},{"id":"mrc__share_title","name":"mrc__share_title","content":"Koszulity of cohomology = K(π,1)-ness + quasi-formality"},{"id":"itemprop","itemprop":"name","content":"Koszulity of cohomology = K(π,1)-ness + quasi-formality"},{"id":"twitter:title","name":"twitter:title","content":"Koszulity of cohomology = K(π,1)-ness + quasi-formality"},{"id":"description","name":"description","content":"This paper is a greatly expanded version of [37, Section 9.11]. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented."},{"id":"og:description","property":"og:description","content":"This paper is a greatly expanded version of [37, Section 9.11]. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented."},{"id":"mrc__share_description","name":"mrc__share_description","content":"This paper is a greatly expanded version of [37, Section 9.11]. A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented."},{"id":"description","itemprop":"description","content":"This paper is a greatly expanded version of [37, Section 9.11]. 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