Integral cohomology groups of real toric manifolds and small covers

Li Cai; Suyoung Choi

doi:10.17323/1609-4514-2021-21-3-467-492

Integral cohomology groups of real toric manifolds and small covers

Li Cai
, Suyoung Choi

Department of Pure Mathematics

Ajou University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

For a simplicial complex K with m vertices, there is a canonical Z^m2-space known as a real moment angle complex RZ_K. In this paper, we consider the quotient spaces Y = RZ_K/Z^k2, where K is a pure shellable complex and Z^k2 ⊂ Z^m2 is a maximal free action on RZ_K. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of Y by using the PL cell decomposition obtained from a shelling of K. In addition, we compute the Bockstein spectral sequence of Y explicitly.

Original language	English
Pages (from-to)	467-492
Number of pages	26
Journal	Moscow Mathematical Journal
Volume	21
Issue number	3
DOIs	https://doi.org/10.17323/1609-4514-2021-21-3-467-492
Publication status	Published - 1 Jul 2021

Keywords

Bockstein homo-morphisms
Cohomology groups
Real toric manifold
Small cover

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10.17323/1609-4514-2021-21-3-467-492

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title = "Integral cohomology groups of real toric manifolds and small covers",

abstract = "For a simplicial complex K with m vertices, there is a canonical Zm2-space known as a real moment angle complex RZK. In this paper, we consider the quotient spaces Y = RZK/Zk2, where K is a pure shellable complex and Zk2 ⊂ Zm2 is a maximal free action on RZK. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of Y by using the PL cell decomposition obtained from a shelling of K. In addition, we compute the Bockstein spectral sequence of Y explicitly.",

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AU - Choi, Suyoung

PY - 2021/7/1

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N2 - For a simplicial complex K with m vertices, there is a canonical Zm2-space known as a real moment angle complex RZK. In this paper, we consider the quotient spaces Y = RZK/Zk2, where K is a pure shellable complex and Zk2 ⊂ Zm2 is a maximal free action on RZK. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of Y by using the PL cell decomposition obtained from a shelling of K. In addition, we compute the Bockstein spectral sequence of Y explicitly.

AB - For a simplicial complex K with m vertices, there is a canonical Zm2-space known as a real moment angle complex RZK. In this paper, we consider the quotient spaces Y = RZK/Zk2, where K is a pure shellable complex and Zk2 ⊂ Zm2 is a maximal free action on RZK. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of Y by using the PL cell decomposition obtained from a shelling of K. In addition, we compute the Bockstein spectral sequence of Y explicitly.

KW - Bockstein homo-morphisms

KW - Cohomology groups

KW - Real toric manifold

KW - Small cover

UR - https://www.scopus.com/pages/publications/85108944183

U2 - 10.17323/1609-4514-2021-21-3-467-492

DO - 10.17323/1609-4514-2021-21-3-467-492

M3 - Article

AN - SCOPUS:85108944183

SN - 1609-3321

VL - 21

SP - 467

EP - 492

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 3

ER -

Integral cohomology groups of real toric manifolds and small covers

Abstract

Keywords

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