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Groups and Complements of Knots

Published online by Cambridge University Press:  20 November 2018

C. D. Feustel  and
Wilbur Whitten
C. D. Feustel
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
Wilbur Whitten
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
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We investigate the extent to which knot groups determine knot manifolds and knot types. Let Ki(i = 1, 2) denote a tame knot in S3, let Ci denote a Ki-knot manifold, and assume that Π1(C1) ≈ Π1(C2). The first named author recently showed (in [6]) that, if C1 has no essential annulus, then C1 ≅ C2, and so K1 and K2 are equivalent, if K1 has property P.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1284 - 1295
Copyright
Copyright © Canadian Mathematical Society 1978

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