Smith theory revisited
type: Item
instance of: scholarly article
title: Smith theory revisited
zbMATH Open document ID: 0675.55011
DOI: 10.2307/1971419
author: William Dwyer
author: C. W. Wilkerson
published in: Annals of Mathematics. Second Series
publication date: 1988-01-01T00:00:00Z
review text: Let G be an elementary abelian p-group and X a finite CW-complex on which G acts. In this very elegant paper the authors show an explicit functorial description of the mod p-cohomology of the fixed point set \(H^*(X^ G)\) in terms of \(H^*(EG\times_ GX)\) considered both as a module over the Steenrod algebra and over the cohomology ring \(H^*(BG)\). The starting point for this work was the classical localization theorem in equivariant cohomology. As an application the authors describe mod 2-cohomology of fixed point sets of involutions on cohomology real projective space.
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 4105867
zbMATH Keywords: fixed point set
zbMATH Keywords: Steenrod algebra
zbMATH Keywords: localization
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: real projective space
reviewed by: Stefan Jackowski
MaRDI profile type: Publication
OpenAlex ID: W2328097807
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description: scientific article; zbMATH DE number 4105867