Combinatorial proofs for basic properties of Ozsvath-Szabo invariant

TL;DR

This paper uses combinatorial methods to prove fundamental properties of the Ozsvath-Szabo invariant by applying algorithms to stabilizations of open books, advancing the understanding of Heegaard Floer homology.

Contribution

It introduces a combinatorial approach to establish basic properties of the Ozsvath-Szabo invariant through stabilization techniques.

Findings

Proved fundamental properties of Ozsvath-Szabo invariant.

Applied combinatorial algorithms to open book stabilizations.

Enhanced computational methods for Heegaard Floer homology.

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.