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 CW-complex homotopy equivalent to a product of spheres.