The University of Southampton
University of Southampton Institutional Repository

Groups acting on Cantor sets and the end structure of graphs

Groups acting on Cantor sets and the end structure of graphs
Groups acting on Cantor sets and the end structure of graphs
We describe a variation of the Bergman norm for the algebra of cuts of a connected graph admitting a cofinite group action. By a construction of Dunwoody, this enables us to obtain nested generating sets for invariant subalgebras. We describe a few applications, in particular, to convergence groups acting on Cantor sets. Under certain finiteness assumptions one can deduce that such actions are necessarily geometrically finite, and hence arise as the boundaries of relatively hyperbolic groups. Similar results have already been obtained by Gerasimov by other methods. One can also use these techniques to give an alternative approach to the Almost Stability Theorem of Dicks and Dunwoody.
0030-8730
31-60
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143

Bowditch, Brian H. (2002) Groups acting on Cantor sets and the end structure of graphs. Pacific Journal of Mathematics, 207 (1), 31-60.

Record type: Article

Abstract

We describe a variation of the Bergman norm for the algebra of cuts of a connected graph admitting a cofinite group action. By a construction of Dunwoody, this enables us to obtain nested generating sets for invariant subalgebras. We describe a few applications, in particular, to convergence groups acting on Cantor sets. Under certain finiteness assumptions one can deduce that such actions are necessarily geometrically finite, and hence arise as the boundaries of relatively hyperbolic groups. Similar results have already been obtained by Gerasimov by other methods. One can also use these techniques to give an alternative approach to the Almost Stability Theorem of Dicks and Dunwoody.

Full text not available from this repository.

More information

Published date: 2002

Identifiers

Local EPrints ID: 29776
URI: http://eprints.soton.ac.uk/id/eprint/29776
ISSN: 0030-8730
PURE UUID: a11a1d39-3871-4378-bc7b-3b5028118f0d

Catalogue record

Date deposited: 11 May 2006
Last modified: 15 Jul 2019 19:08

Export record

Contributors

Author: Brian 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.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

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.

×