Characterizing slopes for torus knots

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 D K₀. 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)(s²-1)=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.