Cosmetic surgeries on knots in S^3
Two Dehn surgeries on a knot are called 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.
© 2015 De Gruyter. Received March 5th 2012, as revised version July 10, 2013. This work was carried out when the first author visited Princeton University. The first author was partially supported by an AIM Five-Year Fellowship and NSF grant number DMS-1021956. The second author was supported by a Simons Postdoctoral Fellowship.
Submitted - 1009.4720v2.pdf
Published - Ni_2015p1.pdf