Bounded geometry in relatively hyperbolic groups

Details Bounded geometry in relatively hyperbolic groups Bounded geometry in relatively hyperbolic groups

2004-11-19

arxiv.org/abs/math/0411435v3

New York J. Math. 11 (2005), pp. 89--95.

Mathematics

Group Theory

Scientific paper

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

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