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Heegaard diagrams and holomorphic disks

Peter Ozsvath·Zoltan Szabo
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Abstract

A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the $g$-fold symmetric product of the Heegaard surface. This leads to a topological invariant for three-manifolds, Heegaard Floer homology, which is functorial under cobordisms. In this survey article, we sketch this construction and describe some of its topological applications.

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Peter Ozsvath, Zoltan Szabo. 2004-03-02. Heegaard diagrams and holomorphic disks. https://arxiv.org/abs/math/0403029

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