Characterizing slopes for torus knots

الأصل · EN

A slope pq is called a characterizing slope for a given knot K₀ in S³ if whenever the pq-surgery on a knot K in S³ is homeomorphic to the pq-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 pq 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 more Heegaard Floer homology techniques.