Heegaard-Floer homologies of (+1) surgeries on torus knots

摘要

We compute the Heegaard-Floer homology of 3_1 ~3(K) (the (+1) surgery on the torus knot T _(p,q)) in terms of the semigroup generated by p and q, and we find a compact formula (involving Dedekind sums) for the corresponding Ozsváth-Szabó d-invariant. We relate the result to known knot invariants of T _(p,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.