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# Boundaries of geometrically finite groups

Bowditch, B.H. (1999) Boundaries of geometrically finite groups. Mathematische Zeitschrift, 230 (3), 509-527.

Record type: Article

## Abstract

We show that the limit set of a relatively hyperbolic group with no separating horoball is locally connected if it is connected. On the other hand, if there is a separating horoball centred on a parabolic point, one obtains a non-trivial splitting of the group over a parabolic subgroup relative to the maximal parabolic subgroups. Together with results from elsewhere, one deduces that if $\Gamma$ is a relatively hyperbolic group such that each maximal parabolic subgroup is one-or-two ended, finitely presented, and contains no infinite torsion subgroup, then the boundary of $\Gamma$ is locally connected if it is connected. As a corollary, we see that the limit set of a geometrically finite group acting on a complete simply connected manifold of pinched negative curvature must be locally connected if it is connected.

Full text not available from this repository.

Published date: 1999

## Identifiers

Local EPrints ID: 29772
URI: http://eprints.soton.ac.uk/id/eprint/29772
ISSN: 0025-5874
PURE UUID: f752ea60-2a98-48e1-952e-40c165c59b46

## Catalogue record

Date deposited: 27 Jul 2006

## Contributors

Author: B.H. Bowditch