# Cosmetic surgeries on knots in $S^3$

@article{Ni2010CosmeticSO,
title={Cosmetic surgeries on knots in \$S^3\$},
author={Yi Ni and Zhongtao Wu},
journal={arXiv: Geometric Topology},
year={2010}
}
• Published 23 September 2010
• Mathematics, Medicine
• arXiv: Geometric Topology
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.
134 Citations
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