Subgroup separability, knot groups and graph manifolds
Authors:
Graham A. Niblo and Daniel T. Wise
Journal:
Proc. Amer. Math. Soc. 129 (2001), 685693
MSC (2000):
Primary 20E26, 20E06, 20F34, 57M05, 57M25
Published electronically:
April 27, 2000
MathSciNet review:
1707529
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: This paper answers a question of Burns, Karrass and Solitar by giving examples of knot and link groups which are not subgroupseparable. For instance, it is shown that the fundamental group of the square knot complement is not subgroup separable. Let denote the fundamental group of the link consisting of a chain of circles. It is shown that is not subgroup separable. Furthermore, it is shown that is a subgroup of every known nonsubgroup separable compact 3manifold group. It is asked whether all such examples contain .
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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/S000299390005574X
PII:
S 00029939(00)05574X
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. DMS9627506.
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 2000
American Mathematical Society
