Cosmetic surgeries on knots in $S^3$

Details Cosmetic surgeries on knots in $S^3$ Cosmetic surgeries on knots in $S^3$

2010-09-23

arxiv.org/abs/1009.4720v1

Mathematics

Geometric Topology

16 pages

Scientific paper

Two Dehn surgeries on a knot are called {\it purely cosmetic}, if they yield
manifolds that are homeomorphic as oriented manifolds. Using Heegaard Floer
homology, we give necessary conditions for the existence of purely cosmetic
surgeries on knots in $S^3$. Among other things, we show that the two surgery
slopes must be the opposite of each other.

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