Characterizing slopes for torus knots
نویسندگان
چکیده
A slope p q is called a characterizing slope for a given knot K0 in S if whenever the p q –surgery on a knot K in S 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 Tr;s . We show that any slope p q which is larger than the number 30.r 1/.s 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.
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