Surgery on links containing a cable sublink

Clark, Bradd Evans

doi:10.1090/S0002-9939-1978-0509260-8

Surgery on links containing a cable sublink
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Proc. Amer. Math. Soc. 72 (1978), 587-592 Request permission

Abstract:

In this paper it will be shown that there is an upper bound on the genus of any manifold obtained by Dehn surgery on a given torus link. It is also demonstrated that if L is a link in ${S^3}$ with a cable sublink about the knot k, and surgery on at least two components of the sublink cannot be replaced by surgery on k, then the manifold resulting from surgery on L cannot be simply connected.

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