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Sbornik: Mathematics, 2017, Volume 208, Issue 9, Pages 1261–1281
DOI: https://doi.org/10.1070/SM8782
(Mi sm8782)
 

This article is cited in 1 scientific paper (total in 1 paper)

Locally standard torus actions and sheaves over Buchsbaum posets

A. A. Ayzenberg

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
References:
Abstract: Manifolds with locally standard half-dimensional torus actions represent a large and important class of spaces. Cohomology rings of such manifolds are known in particular cases, but in general even Betti numbers are difficult to compute. Our approach to this problem is the following: we consider the orbit type filtration on a manifold with locally standard action and study the induced spectral sequence in homology. It collapses at the second page only in the case when the orbit space is homologically trivial. The cohomology ring in this case has already been computed. Nevertheless, we can completely describe the spectral sequence under more general assumptions, namely when all proper faces of the orbit space are acyclic. The theory of sheaves and cosheaves on finite partially ordered sets is used in the computation. We establish generalizations of the Poincare duality and the Zeeman-McCrory spectral sequence for sheaves of ideals of exterior algebras.
Bibliography: 15 titles.
Keywords: locally standard action, manifold with corners, simplicial poset, sheaf over poset, Zeeman-McCrory spectral sequence.
Funding agency Grant number
Russian Science Foundation 14-11-00414
This research was funded by a grant of the Russian Science Foundation (project no. 14-11-00414).
Received: 08.07.2016 and 21.05.2017
Bibliographic databases:
Document Type: Article
UDC: 515.145
MSC: Primary 57N65, 55R20; Secondary 55R91, 18F20, 55N30, 55U30, 18G40
Language: English
Original paper language: Russian
Citation: A. A. Ayzenberg, “Locally standard torus actions and sheaves over Buchsbaum posets”, Sb. Math., 208:9 (2017), 1261–1281
Citation in format AMSBIB
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\by A.~A.~Ayzenberg
\paper Locally standard torus actions and sheaves over Buchsbaum posets
\jour Sb. Math.
\yr 2017
\vol 208
\issue 9
\pages 1261--1281
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Linking options:
  • https://www.mathnet.ru/eng/sm8782
  • https://doi.org/10.1070/SM8782
  • https://www.mathnet.ru/eng/sm/v208/i9/p3
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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