 

François Dahmani and Asli Yaman
Bounded geometry in relatively hyperbolic groups


Published: 
March 21, 2005

Keywords: 
Relatively hyperbolic groups, Margulis Lemma, Bounded geometry, asymptotic dimension. 
Subject: 
20F69 


Abstract
If a group is relatively
hyperbolic, the parabolic subgroups are virtually nilpotent if and
only if there exists a hyperbolic space with bounded geometry on
which it acts geometrically finitely.
This provides, via the embedding theorem of M. Bonk and O. Schramm,
a very short proof of the finiteness of asymptotic dimension for such
groups (which is known to imply Novikov conjectures).


Acknowledgements
F. Dahmani acknowledges support of the FIM ETH, Zürich.
A. Yaman acknowledges support of the Institute of Mathematics of the University of Bonn and ETH, Zürich. This work was partially done when she was visiting the ETH


Author information
François Dahmani:
Labo. E. Picard, Univ. P.Sabatier, 118 Route de Narbonne, F31062 Toulouse, France.
dahmani@picard.upstlse.fr
http://picard.upstlse.fr/~dahmani/
Asli Yaman:
IHES Le BoisMarie, 35, route de Chartres F91440, BuressurYvette, France

