Cable knots do not admit cosmetic surgeries

Abstract

Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in $S^3$ do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for cable knots.

arXiv comment9 pages

References in corpus (2)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus

Cited by in corpus (1)

• Cosmetic operations and Khovanov multicurves