Constructing homologically trivial actions on products of spheres

Abstract

We prove that if a finite group G has a representation with fixity f, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of f + 1 spheres. This shows, in particular, that every finite group acts freely and homologically trivially on some finite CWcomplex homotopy equivalent to a product of spheres.