English

Heegaard diagrams and holomorphic disks

Geometric Topology 2007-05-23 v1 Symplectic Geometry

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 gg-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.

Keywords

Cite

@article{arxiv.math/0403029,
  title  = {Heegaard diagrams and holomorphic disks},
  author = {Peter Ozsvath and Zoltan Szabo},
  journal= {arXiv preprint arXiv:math/0403029},
  year   = {2007}
}

Comments

41 pages, 10 figures

R2 v1 2026-07-22T17:03:02.360Z