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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Band sums of links which yield composite links. The cabling conjecture for strongly invertible knots


Author: Mario Eudave Muñoz
Journal: Trans. Amer. Math. Soc. 330 (1992), 463-501
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 1112545
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Abstract: We consider composite links obtained by bandings of another link. It is shown that if a banding of a split link yields a composite knot then there is a decomposing sphere crossing the band in one arc, unless there is such a sphere disjoint from the band. We also prove that if a banding of the trivial knot yields a composite knot or link then there is a decomposing sphere crossing the band in one arc. The last theorem implies, via double branched covers, that the only way we can get a reducible manifold by surgery on a strongly invertible knot is when the knot is cabled and the surgery is via the slope of the cabling annulus.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1112545-X
PII: S 0002-9947(1992)1112545-X
Keywords: Band sum, banding, composite knot and link, decomposing sphere, split link, sutured manifold, surgery on knots
Article copyright: © Copyright 1992 American Mathematical Society