An elementary approach to some aspects of Heegaard Floer homology

dc.contributor.advisorGay, David T.en_ZA
dc.contributor.advisorGilmour Christopheren_ZA
dc.contributor.authorRavelomanana, Huygens Christianen_ZA
dc.date.accessioned2016-03-04T16:34:27Z
dc.date.available2016-03-04T16:34:27Z
dc.date.issued2010en_ZA
dc.description.abstractHeegaard 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.en_ZA
dc.identifier.apacitationRavelomanana, H. C. (2010). <i>An elementary approach to some aspects of Heegaard Floer homology</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17446en_ZA
dc.identifier.chicagocitationRavelomanana, Huygens Christian. <i>"An elementary approach to some aspects of Heegaard Floer homology."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010. http://hdl.handle.net/11427/17446en_ZA
dc.identifier.citationRavelomanana, H. 2010. An elementary approach to some aspects of Heegaard Floer homology. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ravelomanana, Huygens Christian AB - 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. DA - 2010 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2010 T1 - An elementary approach to some aspects of Heegaard Floer homology TI - An elementary approach to some aspects of Heegaard Floer homology UR - http://hdl.handle.net/11427/17446 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17446
dc.identifier.vancouvercitationRavelomanana HC. An elementary approach to some aspects of Heegaard Floer homology. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17446en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleAn elementary approach to some aspects of Heegaard Floer homologyen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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