Geometry & Topology

Cosmetic surgery in L–space homology spheres

Zhongtao Wu

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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.

Article information

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

Received: 4 October 2010
Revised: 11 April 2011
Accepted: 3 May 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Dehn surgery cosmetic surgery Heegaard Floer homology


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

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