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Published: 
January 3, 2002

Keywords: 
universal space for proper actions, Rips complex, word
hyperbolic group, Gromov hyperbolic group, fixed point set,
conjugacy classes of finite subgroups, finiteness properties for
universal spaces, classifying space for proper actions, GCWcomplex

Subject: 
20F67, 55R35, 57M07

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.}

Acknowledgments:
The first author has been supported by the DAAD
Author information:
David Meintrup:
Universit\"at der Bundeswehr, M\"unchen, Germany
david.meintrup@unibwmuenchen.de
Thomas Schick :
Universit\"at G\"ottingen, Germany
schick@unimath.gwdg.de
www.unimath.gwdg.de/schick/
 