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Toric objects associated with the dodecahedron
Filomat. 2020. Vol. 34. No. 7. P. 2329–2356.
Baralic D., Grbic J., Limonchenko I., Vucic A.
In this paper we illustrate a tight interplay between homotopy theory and combinatorics
within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects
associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and
real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related
small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds
over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of
the Poincar´e series of the corresponding Pontryagin algebra.
Keywords: Massey productsмомент-угол-комплексквазиторическое многообразиеQuasitoric manifoldsпроизведение Массиmoment-angle-complex
Publication based on the results of:
Шиманогов И. Н., Vyalyi M., Дискретный анализ и исследование операций 2025 Т. 32 № 4 С. 213–230
A well-studied class of algorithmic problems is that of regular realizability: checking the non-emptiness of the intersection of a regular language with a given language. This problem has a natural algebraic interpretation: verifying whether an element of a Boolean algebra belongs to the kernel of a certain homomorphism. This motivates the consideration of an analogous ...
Added: July 12, 2026
Rybakov M., Annals of Pure and Applied Logic 2026 Vol. 177 Article 103811
The paper presents a solution to the question about the decidability of the two-variable fragment of the superintuitionistic predicate logic QLC defined by the class of linear Kripke frames, which is also the ‘superintuitionistic’ fragment of the modal predicate logic QS4.3, under the Gödel translation. We prove that the fragment is undecidable. The result remains true for the ...
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Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
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 ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Bahri A., Limonchenko I., Panov T. et al., Discrete and Computational Geometry 2026 Vol. 76 P. 313–338
We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris–Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes. ...
Added: October 26, 2025
Buchstaber V. M., Popelensky T., Успехи математических наук 2024 Т. 79 № 4(478) С. 5–94
Развита теория триградуированной спектральной последовательности Бухштабера Bss для градуированных алгебр Хопфа. Показано, что ее дифференциалы задают возрастающую исчерпывающую фильтрацию как новую структуру в когомологиях этих алгебр. Для ряда известных алгебр Хопфа введенная структура описана в явном виде. На тензорной алгебре T(sExt1,∗A(k,k))надстройки над пространством одномерных когомологий алгебры Хопфа A, заданной над полем k, дана конструкция частичных и многозначных операций Bssp, p⩾1, в терминах которых описаны дифференциалы ...
Added: June 30, 2025
Fedor Vylegzhanin, Yakov Veryovkin, / Series math "arxiv.org". 2025.
Added: April 15, 2025
Limonchenko I., Sergeev M., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 326 С. 275–292
Вычислены вещественные и комплексные числа Бухштабера для всех сфер Бира. В размерности 22 найдены все 13 различных комбинаторных типов сфер Бира, и показано, что 12 из них представимы нерв-комплексами нестоэдров, а оставшийся — нерв-комплексом обобщенного пермутоэдра. В качестве приложения полученных результатов построен нормальный веер для каждого из найденных 13 многогранников Дельзанта, вычислены кольца когомологий соответствующих неособых проективных торических многообразий и ...
Added: January 16, 2025
Ivan Limonchenko, Taras Panov, Song J. et al., Advances in Mathematics 2023 Vol. 432 Article 109274
We put a cochain complex structure CH*(Z_K) on the cohomology of a moment-angle complex Z_K and call the resulting cohomology the double cohomology, HH*(Z_K). We give three equivalent definitions for the differential, and compute HH*(Z_K) for a family of simplicial complexes containing clique complexes of chordal graphs. ...
Added: October 25, 2023
Khovanskii A., Limonchenko I., Monin L., Filomat 2022 Vol. 36 No. 19 P. 6513–6537
The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the cohomology ring of toric variety as a quotient of the ring of differential operators with constant ...
Added: June 1, 2023
Panov T., Зейникешева И. К., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 157–167
We compute the equivariant cohomology $H^*_{T_I}(Z_K)$ of moment-angle complexes $Z_K$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for the equivariant formality of $Z_K$ and obtain specifications for the cases of flag complexes and graphs. ...
Added: November 11, 2022
Limonchenko I., Solomadin G., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 132–156
In this paper we prove that the quotient of any real or complex moment-angle complex by any closed subgroup in the naturally acting compact torus on it is equivariantly homotopy equivalent to the homotopy colimit of a certain toric diagram. For any quotient we prove an equivariant homeomorphism generalizing the well-known Davis-Januszkiewicz construction for quasitoric ...
Added: October 15, 2022
Limonchenko I., Panov T., Успехи математических наук 2022 Т. 77 № 4 С. 203–204
We 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 ...
Added: September 8, 2022
Massey Products in the Cohomology of the Moment-Angle Manifolds Corresponding to Pogorelov Polytopes
E. G. Zhuravleva, Mathematical notes 2019 Vol. 105 No. 4 P. 519–527
Nontrivial 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 ...
Added: October 31, 2021
Limonchenko I., Millionshchikov D., , in: Contemporary Mathematics, Topology, Geometry, and Dynamics V.A.Rokhlin-MemorialVol. 772.: United States of America: American Mathematical Society, 2021. P. 209–240.
Added: October 13, 2021
Solomadin G., Journal of the Mathematical Society of Japan 2020 Vol. 3 P. 765–776
In the present paper we construct two new explicit complex bordisms between any two projective bundles over $\mathbb{C} P^1$ of the same complex dimension, including the Milnor hypersurface $H_{1,n}$ and $\mathbb{C} P^1\times \mathbb{C} P^{n-1}$. These constructions reduce the bordism problem to the null-bordism of some projective bundle over $\mathbb{C} P^1$ with the non-standard stably complex ...
Added: September 20, 2021