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.
685-693
Niblo, Graham A.
43fe9561-c483-4cdf-bee5-0de388b78944
Wise, Daniel T.
35c1ac73-ebb5-4361-9df7-8e82e48ef0b5
2001
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), .
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.
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niblo_wise_subgpsep.pdf
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Published date: 2001
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Publishers Item Identifier (PII): S 0002-9939(00)05574-X
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Local EPrints ID: 29816
URI: http://eprints.soton.ac.uk/id/eprint/29816
ISSN: 0002-9939
PURE UUID: 69ad690d-524c-4059-9cc5-e118fbc776ec
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 02:44
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Author:
Daniel T. Wise
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