Heegaard diagrams and holomorphic disks

2004/03/02 by Peter Ozsváth, Peter Ozsvath, Zoltán Szabó +3
Mathematics · #53D40 #57M27 #57R58 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53D40 #msc:57M27 #msc:57R58

paper · pdf · doi:10.48550/arxiv.math/0403029

41 pages, 10 figures

arxiv created 2004/03/02 · openalex publication_date 2004/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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