Bounded geometry in relatively hyperbolic groups
Group Theory
2007-05-23 v3 Geometric Topology
Abstract
We prove that, 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, by use of M. Bonk and O. Schramm embedding theorem, a very short proof of the finiteness of asymptotic dimension of relatively hyperbolic groups with virtually nilpotent parabolic subgroups (which is known to imply Novikov conjectures
Cite
@article{arxiv.math/0411435,
title = {Bounded geometry in relatively hyperbolic groups},
author = {F. Dahmani and A. Yaman},
journal= {arXiv preprint arXiv:math/0411435},
year = {2007}
}