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Bounded geometry in relatively hyperbolic groups

F. Dahmani·A. Yaman
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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

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F. Dahmani, A. Yaman. 2005-01-31. Bounded geometry in relatively hyperbolic groups. https://arxiv.org/abs/math/0411435

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