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 sep...

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Bibliographic Details
Main Authors: Niblo, Graham A. (Author), Wise, Daniel T. (Author)
Format: Article
Language:English
Published: 2001.
Subjects:
Online Access:Get fulltext
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100 1 0 |a Niblo, Graham A.  |e author 
700 1 0 |a Wise, Daniel T.  |e author 
245 0 0 |a Subgroup separability, knot groups, and graph manifolds 
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856 |z Get fulltext  |u https://eprints.soton.ac.uk/29816/1/niblo_wise_subgpsep.pdf 
520 |a 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. 
655 7 |a Article