Groups and Complements of Knots
- 1 December 1978
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 30 (6) , 1284-1295
- https://doi.org/10.4153/cjm-1978-105-0
Abstract
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.Keywords
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