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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 286, Pages 144–206
DOI: https://doi.org/10.1134/S037196851403008X
(Mi tm3559)
 

This article is cited in 9 scientific papers (total in 9 papers)

Buchstaber invariant theory of simplicial complexes and convex polytopes

N. Yu. Erokhovets

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (633 kB) Citations (9)
References:
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.
Received in June 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 286, Pages 128–187
DOI: https://doi.org/10.1134/S008154381406008X
Bibliographic databases:
Document Type: Article
UDC: 515.164.8+514.172.45
Language: Russian
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, Trudy 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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\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
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\yr 2014
\vol 286
\pages 144--206
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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