Poincare duality in P.A. Smith theory
Algebraic Topology
2007-05-23 v1
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.
Cite
@article{arxiv.math/0205227,
title = {Poincare duality in P.A. Smith theory},
author = {Ch. Allday and B. Hanke and V. Puppe},
journal= {arXiv preprint arXiv:math/0205227},
year = {2007}
}
Comments
10 pages, to be published in Proc. AMS