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A Note on Chirally Cosmetic Surgery on Cable Knots

Published online by Cambridge University Press:  29 April 2020

Tetsuya Ito
Tetsuya Ito*
Affiliation:
Department of Mathematics, Kyoto University, Kyoto606-8502, JAPAN
*
e-mail: tetitoh@math.kyoto-u.ac.jp
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Abstract

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.

Keywords

Chirally cosmetic surgerycable knots
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 163 - 173
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

The author has been partially supported by JSPS KAKENHI Grant Number 19K03490, 16H02145.

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