Heegaard Floer homologies for (+1) surgeries on torus knots

الأصل · EN

We compute the Heegaard Floer homology of S³₁(K) (the (+1) surgery on the torus knot Tₚ,q) in terms of the semigroup generated by p and q, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsvath--Szabo d-invariant. We relate the result to known knot invariants of Tₚ,q as the genus and the Levine--Tristram signatures. Furthermore, we emphasize the striking resemblance between Heegaard Floer homologies of (+1) and (-1) surgeries on torus knots. This relation is best seen at the level of τ functions.