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# Peripheral splittings of groups

Bowditch, B.H. (1997) Peripheral splittings of groups. Transactions of the American Mathematical Society, 353, 4057-4082.

Record type: Article

## Abstract

We define the notion of a peripheral splitting'' of a group. This is essentially a representation of the group as the fundamental group of a bipartite graph of groups, where all the vertex groups of one colour are held fixed --- the peripheral subgroups''. We develop the theory of such splittings and prove an accessibility result. The main application is to relatively hyperbolic groups with connected boundary, where the peripheral subgroups are precisely the maximal parabolic subgroups. We show that if such a group admits a non-trivial peripheral splitting, then its boundary has a global cut point. Morever, the non-peripheral vertex groups of such a splitting are themselves relatively hyperbolic. These results, together with results from elsewhere, show that under modest constraints on the peripheral subgroups, the boundary of relatively hyperbolic group is locally connected if it is connected. In retrospect, one further deduces that the set of global cut points in such a boundary has a simplicial treelike structure.

Full text not available from this repository.

Published date: 1997

## Identifiers

Local EPrints ID: 29770
URI: https://eprints.soton.ac.uk/id/eprint/29770
ISSN: 0002-9947
PURE UUID: 482c8c4f-33e2-48b5-be4a-3f2d5810f6f0

## Catalogue record

Date deposited: 21 Dec 2006

## Contributors

Author: B.H. Bowditch