Volume 15, issue 2 (2011)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Cosmetic surgery in L–space homology spheres

Zhongtao Wu

Geometry & Topology 15 (2011) 1157–1168
Abstract

Let K be a nontrivial knot in S3, and let r and r be two distinct rational numbers of same sign. We prove that there is no orientation-preserving homeomorphism between the manifolds Sr3(K) and Sr3(K). 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
References
Publication
Received: 4 October 2010
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/