Characterizing slopes for torus knots

Ni, Yi¹ ; Zhang, Xingru²

¹Department of Mathematics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA
²Department of Mathematics, University at Buffalo, Buffalo, NY 14260, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1249-1274

Résumé

A slope p q is called a characterizing slope for a given knot K0 in S3 if whenever the p q–surgery on a knot K in S3 is homeomorphic to the p q–surgery on K0 via an orientation preserving homeomorphism, then K = K0. In this paper we try to find characterizing slopes for torus knots Tr,s. We show that any slope p q which is larger than the number 30(r2 − 1)(s2 − 1)∕67 is a characterizing slope for Tr,s. The proof uses Heegaard Floer homology and Agol–Lackenby’s 6–theorem. In the case of  T5,2, we obtain more specific information about its set of characterizing slopes by applying further Heegaard Floer homology techniques.

Détail

DOI : 10.2140/agt.2014.14.1249

Classification : 57M27, 57R58, 57M50
Keywords: Dehn surgery, torus knots, characterizing slopes, Heegaard Floer homology

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