## Geometry & Topology

### Cosmetic surgery in L–space homology spheres

Zhongtao Wu

#### 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 $Sr′3(K)$. We further generalize this uniqueness result to knots in arbitrary L–space homology spheres.

#### Article information

Source
Geom. Topol., Volume 15, Number 2 (2011), 1157-1168.

Dates
Revised: 11 April 2011
Accepted: 3 May 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732314

Digital Object Identifier
doi:10.2140/gt.2011.15.1157

Mathematical Reviews number (MathSciNet)
MR2831258

Zentralblatt MATH identifier
1226.57016

#### Citation

Wu, Zhongtao. Cosmetic surgery in L–space homology spheres. Geom. Topol. 15 (2011), no. 2, 1157--1168. doi:10.2140/gt.2011.15.1157. https://projecteuclid.org/euclid.gt/1513732314

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