Smith theory revisited. (English) Zbl 0675.55011

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.
Reviewer: S.Jackowski


55S10 Steenrod algebra
57S17 Finite transformation groups
55N91 Equivariant homology and cohomology in algebraic topology
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