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 Tr. Mat. Inst. Steklova, 2014, Volume 286, Pages 144–206 (Mi tm3559)

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
\Bibitem{Ero14} \by N.~Yu.~Erokhovets \paper Buchstaber invariant theory of simplicial complexes and convex polytopes \inbook Algebraic topology, convex polytopes, and related topics \bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday \serial Tr. Mat. Inst. Steklova \yr 2014 \vol 286 \pages 144--206 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3559} \crossref{https://doi.org/10.1134/S037196851403008X} \elib{https://elibrary.ru/item.asp?id=22020637} \transl \jour Proc. Steklov Inst. Math. \yr 2014 \vol 286 \pages 128--187 \crossref{https://doi.org/10.1134/S008154381406008X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000343605900008} \elib{https://elibrary.ru/item.asp?id=24022301} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919784558} 

• http://mi.mathnet.ru/eng/tm3559
• https://doi.org/10.1134/S037196851403008X
• http://mi.mathnet.ru/eng/tm/v286/p144

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This publication is cited in the following articles:
1. I. Yu. Limonchenko, “Semeistva minimalno negolodovskikh kompleksov i poliedralnye proizvedeniya”, Dalnevost. matem. zhurn., 15:2 (2015), 222–237
2. V. M. Buchstaber, A. A. Kustarev, “Embedding theorems for quasi-toric manifolds given by combinatorial data”, Izv. Math., 79:6 (2015), 1157–1183
3. Ayzenberg A., “Buchstaber Invariant, Minimal Non-Simplices and Related”, Osaka J. Math., 53:2 (2016), 377–395
4. 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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