New York Journal of Mathematics
Volume 8 (2002) 1-7


David Meintrup and Thomas Schick

A Model for the Universal Space for Proper Actions of a Hyperbolic Group

Published: January 4, 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, G-CW-complex
Subject: 20F67, 55R35, 57M07

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 PH 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

Author information

David Meintrup:
Universität der Bundeswehr, München, Germany

Thomas Schick:
Universität Göttingen, Germany