Smooth toral actions
type: Item
instance of: scholarly article
title: Smooth toral actions
zbMATH Open document ID: 0536.57020
DOI: 10.1016/0040-9383(83)90012-5
author: Jeanne Duflot
published in: Topology
publication date: 1983-01-01T00:00:00Z
review text: Given a smooth action of an elementary abelian group A on a smooth manifold M, the author describes the A-equivariant cohomology of M in terms of the equivariant cohomology of the singular strata provided the set of singular components satisfies a mild finiteness condition. Specifically, there is a filtration of the equivariant cohomology of M whose successive quotients are the equivariant cohomologies of the relevant singular sets. This decomposition yields a product decomposition for the Poincaré series of the equivariant cohomology of M. If the restriction map from equivariant to ordinary cohomology is surjective, then one recovers a result of Borel on the cohomology of the fixed set \(M^ A\), and in addition one obtains a relationship involving the Euler characteristics of M, \(M^ A\), and the intermediate strata of the group action.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 57N80
zbMATH DE Number: 3852045
zbMATH Keywords: smooth action of an elementary abelian group on a smooth manifold
zbMATH Keywords: singular strata
zbMATH Keywords: product decomposition for the Poincaré series of the equivariant cohomology
zbMATH Keywords: cohomology of the fixed set
zbMATH Keywords: Euler characteristics
MaRDI profile type: Publication
full work available at URL: 0040-9383(83)90012-5
OpenAlex ID: W2041166682
description: scientific article; zbMATH DE number 3852045