New York Journal of Mathematics
Volume 11 (2005) 89-95


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

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).


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, F-31062 Toulouse, France.

Asli Yaman:
IHES Le Bois-Marie, 35, route de Chartres F-91440, Bures-sur-Yvette, France