On the contact Ozsvath-Szabo invariant

Details On the contact Ozsvath-Szabo invariant On the contact Ozsvath-Szabo invariant

2007-08-21

arxiv.org/abs/0708.2772v1

Mathematics

Geometric Topology

17 pages, 18 figures

Scientific paper

Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsvath-Szabo invariant is combinatorial once we are given an open book decomposition compatible with a contact structure. The idea is to combine the algorithm of Sarkar and Wang with the recent description of the contact Ozsvath-Szabo invariant due to Honda, Kazez and Matic. Here we simply observe that the hat version of the Heegaard Floer homology group and the contact Ozsvath-Szabo invariant in this group can be combinatorially calculated starting from a contact surgery diagram. We give detailed examples pointing out to some shortcuts in the computations.

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