Combinatorial proofs for basic properties of Ozsvath-Szabo invariant

Abstract

Sarkar and Wang have given a combinatorial algorithm for computing Heegaard Floer homology and Plamenevskaya has improved their method to compute Ozsvath-Szabo invariant. In this paper, applying the combinatorial method to stabilizations of an open book, we prove basic properties of Ozsvath-Szabo invariant.

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• Combinatorial cobordism maps in hat Heegaard Floer theory
• On the contact class in Heegaard Floer homology
• An algorithm for computing some Heegaard Floer homologies
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