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1 results

A Note on Chirally Cosmetic Surgery on Cable Knots
Tetsuya Ito
Journal:

Canadian Mathematical Bulletin / Volume 64 / Issue 1 / March 2021

Published online by Cambridge University Press:

29 April 2020, pp. 163-173

Print publication:

March 2021
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We show that a $(p,q)$-cable of a non-trivial knot K does not admit chirally cosmetic surgeries for $q\neq 2$, or $q=2$ with additional assumptions. In particular, we show that a $(p,q)$-cable of a non-trivial knot K does not admit chirally cosmetic surgeries as long as the set of JSJ pieces of the knot exterior does not contain the $(2,r)$-torus exterior for any r. We also show that an iterated torus knot other than the $(2,p)$-torus knot does not admit chirally cosmetic surgery.