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Poincare duality in P.A. Smith theory

Ch. Allday·B. Hanke·V. Puppe
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Abstract

Let G=S^1, G=Z/p or more generally G be a finite p group, where p is an odd prime number. If G acts on a space whose cohomology ring satisfies Poincare duality (with appropriate coefficients k), we prove a mod 4 congruence between the total Betti number of X^G and a number which depends only on the k[G]-module structure of H^*(X;k). This improves the well known mod 2 congruences that hold for actions on general spaces.

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Ch. Allday, B. Hanke, V. Puppe. 2002-05-22. Poincare duality in P.A. Smith theory. https://arxiv.org/abs/math/0205227

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