Cosmetic surgeries on genus one knots

Abstract

In this paper, we prove that there are no truly cosmetic surgeries on genus one classical knots. If the two surgery slopes have the same sign, we give the only possibilities of reflectively cosmetic surgeries. The result is an application of Heegaard Floer theory and number theory.

This is the version published by Algebraic & Geometric Topology on 4 October 2006

References in corpus (4)

• On the Floer homology of plumbed three-manifolds
• Longitude Floer homology and the Whitehead double
• On knot Floer homology and cabling
• Sutured Heegaard diagrams for knots

Cited by in corpus (7)

• Knot Floer homology and rational surgeries
• Cosmetic Surgery in Integral Homology $L$-Spaces
• The Legendrian knot complement problem
• Mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$
• Purely cosmetic surgeries and pretzel knots
• 3-braid knots do not admit purely cosmetic surgeries
• Cosmetic operations and Khovanov multicurves