Twisting operations and composite knots

Teragaito, Masakazu

doi:10.1090/S0002-9939-1995-1254855-X

Twisting operations and composite knots
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by Masakazu Teragaito

Proc. Amer. Math. Soc. 123 (1995), 1623-1629

DOI: https://doi.org/10.1090/S0002-9939-1995-1254855-X

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Abstract:

Suppose that a composite knot K in ${S^3}$ can be changed to a trivial knot by 1/n-surgery along a trivial loop C. We show that $|n| \leq 2$. Moreover, if there is a decomposing sphere of K which meets C in two points, then $|n| \leq 1$.

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