Cosmetic surgery in L–space homology spheres

Wu, Zhongtao¹

¹ Department of Mathematics, California Institute of Technology, Pasadena CA 91125, USA

Geometry & topology, Tome 15 (2011) no. 2, pp. 1157-1168.

Résumé

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.

Détail

DOI : 10.2140/gt.2011.15.1157

Classification : 57M25, 57M27
Keywords: Dehn surgery, cosmetic surgery, Heegaard Floer homology

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