A Note on Chirally Cosmetic Surgery on Cable Knots. Issue 1 (29th March 2021)

• Record Type: Journal Article
• Authors: Ito, Tetsuya
• Is Part Of: Canadian mathematical bulletin =. Volume 64:Issue 1(2021)
• Page Start: 163
• Page End: 173
• Publication Date: 2021-03-29
• Subjects: 57K30, -- 57K10; Chirally cosmetic surgery, -- cable knots; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439520000338
• Languages: English
• ISSNs: 0008-4395

Abstract

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.