Torus and ℤ/p actions on manifolds

Adam S. Sikora

doi:10.1016/j.top.2003.10.009

Torus and ℤ/p actions on manifolds

Adam S. Sikora

Mathematics

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

4 Scopus citations

Abstract

Let G be either a finite cyclic group of prime order or S¹. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M, then each term of the Leray spectral sequence of the map M×_GEG→BG satisfies a properly defined "Poincaré duality". As a consequence of this fact we obtain new results relating the cohomology groups of M and M^G. We apply our results to study group actions on 3-manifolds.

Original language	English
Pages (from-to)	725-748
Number of pages	24
Journal	Topology
Volume	43
Issue number	3
DOIs	https://doi.org/10.1016/j.top.2003.10.009
State	Published - May 2004

Keywords

Cyclic group action
Equivariant cohomology
Leray spectral sequence
Leray-Serre spectral sequence
Poincaré duality
Torus action

Access to Document

10.1016/j.top.2003.10.009

Cite this

@article{0ae0c02bc20e4e518df789b5a20a9ce5,

title = "Torus and ℤ/p actions on manifolds",

abstract = "Let G be either a finite cyclic group of prime order or S1. We show that if G acts on a manifold or, more generally, on a Poincar{\'e} duality space M, then each term of the Leray spectral sequence of the map M×GEG→BG satisfies a properly defined {"}Poincar{\'e} duality{"}. As a consequence of this fact we obtain new results relating the cohomology groups of M and MG. We apply our results to study group actions on 3-manifolds.",

keywords = "Cyclic group action, Equivariant cohomology, Leray spectral sequence, Leray-Serre spectral sequence, Poincar{\'e} duality, Torus action",

author = "Sikora, \{Adam S.\}",

year = "2004",

month = may,

doi = "10.1016/j.top.2003.10.009",

language = "English",

volume = "43",

pages = "725--748",

journal = "Topology",

issn = "0040-9383",

publisher = "Elsevier Ltd",

number = "3",

}

TY - JOUR

T1 - Torus and ℤ/p actions on manifolds

AU - Sikora, Adam S.

PY - 2004/5

Y1 - 2004/5

N2 - Let G be either a finite cyclic group of prime order or S1. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M, then each term of the Leray spectral sequence of the map M×GEG→BG satisfies a properly defined "Poincaré duality". As a consequence of this fact we obtain new results relating the cohomology groups of M and MG. We apply our results to study group actions on 3-manifolds.

AB - Let G be either a finite cyclic group of prime order or S1. We show that if G acts on a manifold or, more generally, on a Poincaré duality space M, then each term of the Leray spectral sequence of the map M×GEG→BG satisfies a properly defined "Poincaré duality". As a consequence of this fact we obtain new results relating the cohomology groups of M and MG. We apply our results to study group actions on 3-manifolds.

KW - Cyclic group action

KW - Equivariant cohomology

KW - Leray spectral sequence

KW - Leray-Serre spectral sequence

KW - Poincaré duality

KW - Torus action

UR - https://www.scopus.com/pages/publications/1542718624

U2 - 10.1016/j.top.2003.10.009

DO - 10.1016/j.top.2003.10.009

M3 - Article

AN - SCOPUS:1542718624

SN - 0040-9383

VL - 43

SP - 725

EP - 748

JO - Topology

JF - Topology

IS - 3

ER -

Torus and ℤ/p actions on manifolds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this