Heegaard diagrams and holomorphic disks

Research paper by Peter Ozsvath, Zoltan Szabo

Indexed on: 02 Mar '04Published on: 02 Mar '04Published in: Mathematics - Geometric Topology


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.