Title: Constructing homologically trivial actions on products of spheres
Authors: {\" O}zg{\" u}n {\" U}nl{\" u} and Erg{\" u}n Yal{\c c}{\i}n
Status: submitted.
Address:
Department of Mathematics, Bilkent University,
06800 Bilkent, Ankara, Turkey
Email1: unluo@fen.bilkent.edu.tr
Email2: yalcine@fen.bilkent.edu.tr
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.