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

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

2011-05-27

arxiv.org/abs/1105.5508v1

Mathematics

Geometric Topology

12 pages, 1 figure

Scientific paper

We compute the Heegaard Floer homology of $S^3_1(K)$ (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 Ozsvath--Szabo 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 $\tau$ functions.

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