Characterizing slopes for torus knots

A slope p q is called a characterizing slope for a given knot K 0 in S 3 if whenever the p q -surgery on a knot K in S 3 is homeomorphic to the p q -surgery on K 0 via an orientation preserving homeomorphism, then K D K 0 . In this paper we try to find characterizing slopes for torus knots T r;s . We show that any slope p q which is larger than the number 30.r 2 1/.s 2 1/=67 is a characterizing slope for T r;s . The proof uses Heegaard Floer homology and Agol-Lackenby's 6-theorem. In the case of T 5;2 , we obtain more specific information about its set of characterizing slopes by applying further Heegaard Floer homology techniques.