A geometric proof of Stallings' Theorem on groups with more than one end
A geometric proof of Stallings' Theorem on groups with more than one end
Stallings showed that a finitely generated group which has more than one end splits as an amalgamated free product or an HNN extension over a finite subgroup. Dunwoody gave a new geometric proof of the theorem for the class of almost finitely presented groups, and separately, using somewhat different methods, generalised it to a larger class of splittings.
Here we adapt the geometric method to the class of finitely generated groups using Sageev's generalisation of Bass Serre theory concerning group pairs with more than one end, and show that this new proof simultaneously establishes Dunwoody's generalisation.
amalgamated free product, bass–serre theory, cat(0) cube complex, ends, hnn extension, singularity obstruction, stallings' theorem
61-76
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
2004
Niblo, Graham
43fe9561-c483-4cdf-bee5-0de388b78944
Abstract
Stallings showed that a finitely generated group which has more than one end splits as an amalgamated free product or an HNN extension over a finite subgroup. Dunwoody gave a new geometric proof of the theorem for the class of almost finitely presented groups, and separately, using somewhat different methods, generalised it to a larger class of splittings.
Here we adapt the geometric method to the class of finitely generated groups using Sageev's generalisation of Bass Serre theory concerning group pairs with more than one end, and show that this new proof simultaneously establishes Dunwoody's generalisation.
Text
Stallingstheorem.pdf
- Author's Original
Other
Stallingsapproved.fdf
- Version of Record
Restricted to Registered users only
Request a copy
More information
Published date: 2004
Keywords:
amalgamated free product, bass–serre theory, cat(0) cube complex, ends, hnn extension, singularity obstruction, stallings' theorem
Identifiers
Local EPrints ID: 29820
URI: http://eprints.soton.ac.uk/id/eprint/29820
PURE UUID: cbc80b1b-53f0-487f-ace8-d0e51ece77e1
Catalogue record
Date deposited: 12 May 2006
Last modified: 16 Mar 2024 02:44
Export record
Altmetrics
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
