A Note on Chirally Cosmetic Surgery on Cable Knots. Issue 1 (29th March 2021) - Ito, Tetsuya
Abstract: We show that a $(p, q)$ -cable of a non-trivial knot K does not admit chirally cosmetic surgeries for $q≠ 2$, 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.