Poincare duality in P.A. Smith theory

الأصل · EN

Let G=S¹, 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 Xᵍ 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.