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Subgroup separability, knot groups and graph manifolds
Author(s):
Graham
A.
Niblo;
Daniel
T.
Wise
Journal:
Proc. Amer. Math. Soc.
129
(2001),
685-693.
MSC (2000):
Primary 20E26, 20E06, 20F34, 57M05, 57M25
Posted:
April 27, 2000
MathSciNet review:
1707529
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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:
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
Posted:
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
Copyright of article:
Copyright
2000,
American Mathematical Society
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