#### Volume 15, issue 2 (2011)

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Cosmetic surgery in L–space homology spheres

### Zhongtao Wu

Geometry & Topology 15 (2011) 1157–1168
##### Abstract

Let $K$ be a nontrivial knot in ${S}^{3}$, and let $r$ and ${r}^{\prime }$ be two distinct rational numbers of same sign. We prove that there is no orientation-preserving homeomorphism between the manifolds ${S}_{r}^{3}\left(K\right)$ and ${S}_{{r}^{\prime }}^{3}\left(K\right)$. We further generalize this uniqueness result to knots in arbitrary L–space homology spheres.

##### Keywords
Dehn surgery, cosmetic surgery, Heegaard Floer homology
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
##### Publication
Revised: 11 April 2011
Accepted: 3 May 2011
Published: 22 July 2011
Proposed: Rob Kirby
Seconded: Danny Calegari, Joan Birman
##### Authors
 Zhongtao Wu Department of Mathematics California Institute of Technology Pasadena CA 91125 USA http://www.its.caltech.edu/~zhongtao/