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 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 non-subgroup separable compact 3-manifold 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/S0002-9939-00-05574-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