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On the contact Ozsváth–Szabó invariant

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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 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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Akademiai Kiado Zrt

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Mathematics

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Studia Scientiarum Mathematicarum Hungarica

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10.1556/SScMath.2009.1115

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