A note on chirally cosmetic surgery on cable knots

Abstract

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

10 pages, 1 figure

References in corpus (1)

• On LMO invariant constraints for cosmetic surgery and other surgery problems for knots in S^{3}

Cited by in corpus (2)

• On constraints for knots to admit chirally cosmetic surgeries and their calculations
• A non-torus positive 2-bridge knot does not admit chirally cosmetic surgeries