 

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, 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.


Acknowledgements
The first author has been supported by the DAAD


Author information
David Meintrup:
Universität der Bundeswehr, München, Germany
david.meintrup@unibwmuenchen.de
Thomas Schick:
Universität Göttingen, Germany
schick@unimath.gwdg.de
http://www.unimath.gwdg.de/schick/

