An elementary approach to some aspects of Heegaard Floer homology
type: CreativeWork
description: Heegaard Floer homology is a new invariant for 3-manifolds and links introduced by Ozsvath and Szabo. It counts pseudo-holomorphic Whitney disks in the symmetric product of the Heegaard surface of the underlying manifold. This thesis is about showing the existence of a natural complex structure on the symmetric product Sym9 (E9) of a surface E9 and mainly studying the moduli space of the set of holomorphic representatives of Whitney disks for special cases of domains from the Heegaard diagram which are bigons and squares. These moduli spaces are relevant for the computation of the boundary map in Heegaard Floer Homology. All of this is done using basic tools from differential topology and complex analysis. We will end this thesis by briefly describing some of the analysis required to ground this work in the more general theory of J-holomorphic curves and partial differential operators.
abstract: Heegaard Floer homology is a new invariant for 3-manifolds and links introduced by Ozsvath and Szabo. It counts pseudo-holomorphic Whitney disks in the symmetric product of the Heegaard surface of the underlying manifold. This thesis is about showing the existence of a natural complex structure on the symmetric product Sym9 (E9) of a surface E9 and mainly studying the moduli space of the set of holomorphic representatives of Whitney disks for special cases of domains from the Heegaard diagram which are bigons and squares. These moduli spaces are relevant for the computation of the boundary map in Heegaard Floer Homology. All of this is done using basic tools from differential topology and complex analysis. We will end this thesis by briefly describing some of the analysis required to ground this work in the more general theory of J-holomorphic curves and partial differential operators.
author: Ravelomanana, Huygens Christian
language: eng
date published: 2010
date modified: 2026-07-24T01:33:45Z
provider: University of Cape Town
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Department of Mathematics and Applied Mathematics

PropertyValue
property ID: Handle
value: http://hdl.handle.net/11427/17446