## 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

### MSC:

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