Heegaard diagrams and holomorphic disks
Abstract
Description
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.
41 pages, 10 figures
41 pages, 10 figures