The University of Southampton
University of Southampton Institutional Repository

The decomposition of 3-dimensional Poincaré complexes

The decomposition of 3-dimensional Poincaré complexes
The decomposition of 3-dimensional Poincaré complexes
We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of S^1 \times S^2. Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.
poincaré complex, graph of groups, tree
232-246
Crisp, J.
92ec42d1-ff21-49cc-aa99-594a35027009
Crisp, J.
92ec42d1-ff21-49cc-aa99-594a35027009

Crisp, J. (2000) The decomposition of 3-dimensional Poincaré complexes. Commentarii Mathematici Helvetici, 75 (2), 232-246.

Record type: Article

Abstract

We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of S^1 \times S^2. Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.

Full text not available from this repository.

More information

Published date: 2000
Keywords: poincaré complex, graph of groups, tree

Identifiers

Local EPrints ID: 29863
URI: https://eprints.soton.ac.uk/id/eprint/29863
PURE UUID: 10fba9b8-93a7-407f-a197-6ef6b5c528e0

Catalogue record

Date deposited: 19 Mar 2007
Last modified: 01 Nov 2018 17:31

Export record

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 https://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.

×