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Tr. Mat. Inst. Steklova, 2014, Volume 286, Pages 144–206
(Mi tm3559)
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This article is cited in 4 scientific papers (total in 4 papers)
Buchstaber invariant theory of simplicial complexes and convex polytopes
N. Yu. Erokhovets Lomonosov Moscow State University, Moscow, Russia
Abstract:
The survey is devoted to the theory of a combinatorial invariant of simple convex polytopes and simplicial complexes that was introduced by V. M. Buchstaber on the basis of constructions of toric topology. We describe methods for calculating this invariant and its relation to other classical and modern combinatorial invariants and constructions, calculate the invariant for special classes of polytopes and simplicial complexes, and find a criterion for this invariant to be equal to a given small number. We also describe a relation to matroid theory, which allows one to apply the results of this theory to the description of the real Buchstaber number in terms of subcomplexes of the Alexander dual simplicial complex.
DOI:
https://doi.org/10.1134/S037196851403008X
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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 286, 128–187
Bibliographic databases:
UDC:
515.164.8+514.172.45 Received in June 2014
Citation:
N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Algebraic topology, convex polytopes, and related topics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 144–206; Proc. Steklov Inst. Math., 286 (2014), 128–187
Citation in format AMSBIB
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\inbook Algebraic topology, convex polytopes, and related topics
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\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 286
\pages 144--206
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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http://mi.mathnet.ru/eng/tm3559https://doi.org/10.1134/S037196851403008X http://mi.mathnet.ru/eng/tm/v286/p144
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V. M. Buchstaber, A. A. Kustarev, “Embedding theorems for quasi-toric manifolds given by combinatorial data”, Izv. Math., 79:6 (2015), 1157–1183
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Ayzenberg A., “Buchstaber Invariant, Minimal Non-Simplices and Related”, Osaka J. Math., 53:2 (2016), 377–395
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Choi S., Park K., “Example of C-Rigid Polytopes Which Are Not B-Rigid”, Math. Slovaca, 69:2 (2019), 437–448
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