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.