2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64122Let 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.10 pages, to be published in Proc. AMSAlgebraic Topology57S10, 57P10, 55N10 (Primary) 55N91 (Secondary)text