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Минимально неголодовы кольца граней и произведения Масси
Успехи математических наук. 2022. Т. 77. № 4. С. 203-204.
Limonchenko I., Panov T.
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 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.
Keywords: Massey productsmoment-angle complexмомент-угол-комплексПроизведения МассиGolod ringsкольца Голода
Publication based on the results of:
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
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
Baralic D., Grbic J., Limonchenko I. et al., Filomat 2020 Vol. 34 No. 7 P. 2329-2356
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. ...
Added: October 12, 2021
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
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
Limonchenko I., Труды Математического института им. В.А. Стеклова РАН 2019 Т. 305 С. 174-196
We construct moment-angle-manifolds over 2-truncated cubes having an arbitrarily large prescribed order of a strictly defined nontrivial Massey product in cohomology. We give a criterion of rational formality for moment-angle-manifolds over graph-associahedra. We obtain a sufficient condition for existence of a strictly defined Massey product in cohomology of a moment-angle-complex in terms of vanishing of ...
Added: September 14, 2019
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1811.02221.
We develop a theory of direct families of polytopes with nontrivial Massey products ...
Added: September 29, 2019
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
Limonchenko I., Chinese Annals of Mathematics. Series B 2017 Vol. 38 No. 6 P. 1287-1302
We compute bigraded Betti numbers of graph-associahedra corresponding to maximal non-connected sets of facets. We obtain a criterion of existence of a triple nontrivial strictly defined Massey product of three-dimensional classes in cohomology of a moment-angle manifold over a graph-associahedron. ...
Added: September 25, 2019
Abramyan S., Panov T., Proceedings of the Steklov Institute of Mathematics 2019 Vol. 1 No. 305 P. 1-21
We study the question of realisability of iterated higher Whitehead products with a given form of nested brackets by simplicial complexes, using the notion of the moment–angle complex $\mathcal{Z_K}$. Namely, we say that a simplicial complex $\mathcal{K}$ realises an iterated higher Whitehead product w if wis a nontrivial element of $\pi_*(\mathcal{Z_K})$. The combinatorial approach to the question of realisability uses the ...
Added: October 28, 2019
Grbić J., Simmons G., Ilyasova M. et al., Proceedings of the Royal Society of Edinburgh: Section A 2022 Vol. 152 No. 1 P. 128-147
We link distinct concepts of geometric group theory and homotopy theory through underlying combinatorics. For a flag simplicial complex $K$, we specify a necessary and sufficient combinatorial condition for the commutator subgroup $RC_K'$ of a right-angled Coxeter group, viewed as the fundamental group of the real moment-angle complex $R_K$, to be a one-relator group; and ...
Added: October 29, 2021
Abramyan S., Siberian Mathematical Journal 2019 Vol. 60 No. 2 P. 185-196
We give an example of a simplicial complex whose corresponding moment-angle complex is homotopy equivalent to a wedge of spheres, but there is a sphere that cannot be realized by any linear combination of iterated higher Whitehead products. Using two explicitly defined operations on simplicial complexes, we prove that there exists a simplicial complex that ...
Added: May 10, 2020
Vylegzhanin F., Proceedings of the Steklov Institute of Mathematics (USA) 2022 Т. 317 С. 64-88
For any flag simplicial complex K, we describe the multigraded Poincaré series, the minimal number of relations, and the degrees of these relations in the Pontryagin algebra of the corresponding moment–angle complex ZK. We compute the LS-category of ZK for flag complexes and give a lower bound in the general case. The key observation is that the Milnor–Moore spectral ...
Added: November 15, 2022
Limonchenko I., Успехи математических наук 2016 Т. 71 № 2 С. 207-208
We give the first example of polyhedral products with nontrivial higher Massey products of any prescribed order in cohomology. ...
Added: September 29, 2019
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
Panov T., Theriault S., Compositio Mathematica 2019 Vol. 155 No. 1 P. 206-228
If K is a simplicial complex on m vertices the flagification of K is the minimal flag complex Kf on the same vertex set that contains K. Letting L be the set of vertices, there is a sequence of simplicial inclusions L→K→Kf. This induces a sequence of maps of polyhedral products (X,A)^L⟶g(X,A)^K⟶f(X,A)^{Kf}. We show that Ωf and Ωf∘Ωg have right homotopy inverses and draw consequences. For a flag complex K the polyhedral product of ...
Added: October 29, 2021
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
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Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
Added: March 9, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
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Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
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Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
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