A note on chirally cosmetic surgery on cable knots

Tetsuya Ito

doi:10.4153/s0008439520000338

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arXiv · 1905.06570

A note on chirally cosmetic surgery on cable knots

Tetsuya Ito

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Abstract

We show that a $(p,q)$-cable of a non-trivial knot $K$ does not admit chirally cosmetic surgery for $q\neq 2$, or $q=2$ with additional assumptions. In particular, we show that $(p,q)$-cable of non-trivial knot $K$ does not admit chirally cosmetic surgery as long as the JSJ piece of knot exterior does not contain $(2,r)$-torus exterior. We also show that an iterated torus knot other than $(2,p)$-torus knot does not admit chirally cosmetic surgery.

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Tetsuya Ito. 2019-05-16. A note on chirally cosmetic surgery on cable knots. https://doi.org/10.4153/s0008439520000338

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