A model for the universal space for proper actions of a hyperbolic group

Abstract:

{ Let $G$ be a word hyperbolic group in the sense of Gromov and $P$ its associated Rips complex. We prove that the fixed point set $P^H$ is contractible for every finite subgroup $H$ of $G$. This is the main ingredient for proving that $P$ is a finite model for the universal space $\eg$ for proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.}

The first author has been supported by the DAAD

David Meintrup:
Universit\"at der Bundeswehr, M\"unchen, Germany
david.meintrup@unibw-muenchen.de

Thomas Schick :
Universit\"at G\"ottingen, Germany
schick@uni-math.gwdg.de
www.uni-math.gwdg.de/schick/