The University of Southampton
University of Southampton Institutional Repository

Peripheral splittings of groups

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

Record type: Article


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.

More information

Published date: 1997


Local EPrints ID: 29770
ISSN: 0002-9947
PURE UUID: 482c8c4f-33e2-48b5-be4a-3f2d5810f6f0

Catalogue record

Date deposited: 21 Dec 2006
Last modified: 17 Jul 2017 15:57

Export record


Author: B.H. Bowditch

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.