The University of Southampton
University of Southampton Institutional Repository

Subgroup separability, knot groups, and graph manifolds

Subgroup separability, knot groups, and graph manifolds
Subgroup separability, knot groups, and graph manifolds
This paper answers a question of Burns, Karrass and Solitar by giving examples of knot and link groups which are not subgroup-separable. For instance, it is shown that the fundamental group of the square knot complement is not subgroup separable. We characterise the Graph Manifolds with subgroup separable fundamental group as precisely the geometric ones, i.e. the Seifert Fibered 3-manifolds and the Sol manifolds, and show that there is a specific non-subgroup separable group which is a subgroup in all other cases.
0002-9939
685-693
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wise, Daniel T.
35c1ac73-ebb5-4361-9df7-8e82e48ef0b5
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wise, Daniel T.
35c1ac73-ebb5-4361-9df7-8e82e48ef0b5

Niblo, Graham A. and Wise, Daniel T. (2001) Subgroup separability, knot groups, and graph manifolds. Proceedings of the American Mathematical Society, 129 (3), 685-693.

Record type: Article

Abstract

This paper answers a question of Burns, Karrass and Solitar by giving examples of knot and link groups which are not subgroup-separable. For instance, it is shown that the fundamental group of the square knot complement is not subgroup separable. We characterise the Graph Manifolds with subgroup separable fundamental group as precisely the geometric ones, i.e. the Seifert Fibered 3-manifolds and the Sol manifolds, and show that there is a specific non-subgroup separable group which is a subgroup in all other cases.

Text
niblo_wise_subgpsep.pdf - Author's Original
Download (175kB)

More information

Published date: 2001
Additional Information: Publishers Item Identifier (PII): S 0002-9939(00)05574-X

Identifiers

Local EPrints ID: 29816
URI: http://eprints.soton.ac.uk/id/eprint/29816
ISSN: 0002-9939
PURE UUID: 69ad690d-524c-4059-9cc5-e118fbc776ec
ORCID for Graham A. Niblo: ORCID iD orcid.org/0000-0003-0648-7027

Catalogue record

Date deposited: 11 May 2006
Last modified: 16 Mar 2024 02:44

Export record

Contributors

Author: Graham A. Niblo ORCID iD
Author: Daniel T. Wise

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.

×