Heegaard Diagrams and Holomorphic Disks

@article{Ozsvth2004HeegaardDA,
  title={Heegaard Diagrams and Holomorphic Disks},
  author={Peter S. Ozsv{\'a}th and Zolt{\'a}n Imre Szab{\'o}},
  journal={arXiv: Geometric Topology},
  year={2004},
  pages={301-348}
}
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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