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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subgroup separability, knot groups and graph manifolds


Authors: Graham A. Niblo and Daniel T. Wise
Journal: Proc. Amer. Math. Soc. 129 (2001), 685-693
MSC (2000): Primary 20E26, 20E06, 20F34, 57M05, 57M25
Published electronically: April 27, 2000
MathSciNet review: 1707529
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Abstract | References | Similar Articles | Additional Information

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. Let $L$ denote the fundamental group of the link consisting of a chain of $4$ circles. It is shown that $L$ is not subgroup separable. Furthermore, it is shown that $L$ is a subgroup of every known non-subgroup separable compact 3-manifold group. It is asked whether all such examples contain $L$.


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Additional Information

Graham A. Niblo
Affiliation: Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton, SO17 1BJ, England
Email: gan@maths.soton.ac.uk

Daniel T. Wise
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
Address at time of publication: Department of Mathematics, White Hall, Cornell University, Ithaca, New York 14853
Email: daniwise@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05574-X
PII: S 0002-9939(00)05574-X
Received by editor(s): April 14, 1998
Received by editor(s) in revised form: May 24, 1999
Published electronically: April 27, 2000
Additional Notes: The second author was supported as an NSF Postdoctoral Fellow under grant no. DMS-9627506.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society