Cosmetic surgeries on knots in $S^3$

Abstract

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield manifolds that are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries on a knot in $S^3$, we show that the two surgery slopes must be the opposite of each other. One ingredient of our proof is a Dehn surgery formula for correction terms in Heegaard Floer homology.

v2: 19 pages, incorporates referee's comments

References in corpus (3)

• Floer homology and knot complements
• Surgery formula for the renormalized Euler characteristic of Heegaard Floer homology
• Cosmetic Surgery in Integral Homology $L$-Spaces

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