Equivariant cohomology of cohomogeneity-one actions: The topological case

被引：1

作者：

Goertsches, Oliver ^{[1
]}

Mare, Augustin-Liviu ^{[2
]}

机构：

[1] Philipps Univ, Fachbereich Math & Informat, Marburg, Germany

[2] Univ Regina, Dept Math & Stat, Regina, SK, Canada

来源：

TOPOLOGY AND ITS APPLICATIONS | 2017年 / 218卷

关键词：

Compact Lie groups; Cohomogeneity one group actions on topological manifolds; Equivariant cohomology; Cohen-Macaulay rings;

D O I：

10.1016/j.topol.2016.12.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for any cohomogeneity-one continuous action of a compact connected Lie group G on a closed topological manifold the equivariant cohomology equipped with its canonical H*(BG)-module structure is Cohen-Macaulay. The proof relies on the structure theorem for these actions recently obtained by Calaz-Garcia and Zarei. We generalize in this way our previous result concerning smooth actions. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：93 / 96

页数：4

共 14 条

[1] Equivariant cohomology of cohomogeneity one actions
Goertsches, Oliver
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TOPOLOGY AND ITS APPLICATIONS, 2014, 167 : 36 - 52
[2] The equivariant cohomology ring of a cohomogeneity-one action
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Geometriae Dedicata, 2019, 203 : 205 - 223
[3] The equivariant cohomology ring of a cohomogeneity-one action
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He, Chen
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[4] TRANSITIVE ACTIONS AND EQUIVARIANT COHOMOLOGY AS AN UNSTABLE A*-ALGEBRA
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[5] Equivariant intersection cohomology of the circle actions
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[6] Equivariant intersection cohomology of the circle actions
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[7] A classification of hyperpolar and cohomogeneity one actions
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[8] Vector fields, torus actions and equivariant cohomology
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PACIFIC JOURNAL OF MATHEMATICS, 2007, 232 (01) : 61 - 76
[9] ON THE EQUIVARIANT COHOMOLOGY OF HYPERPOLAR ACTIONS ON SYMMETRIC SPACES
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DOCUMENTA MATHEMATICA, 2019, 24 : 1657 - 1676
[10] The equivariant cohomology of complexity one spaces
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ENSEIGNEMENT MATHEMATIQUE, 2019, 65 (3-4): : 457 - 485

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