Bounded geometry in relatively hyperbolic groups

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

References in corpus (1)

• Asymptotic dimension of relatively hyperbolic groups

Cited by in corpus (3)

• Quasi-hyperbolic planes in relatively hyperbolic groups
• Groups with no coarse embeddings into hyperbolic groups
• Asymptotic dimension and geometric decompositions in dimensions 3 and 4