An elementary approach to some aspects of Heegaard Floer homology
dc.contributor.advisor | Gay, David T. | en_ZA |
dc.contributor.advisor | Gilmour Christopher | en_ZA |
dc.contributor.author | Ravelomanana, Huygens Christian | en_ZA |
dc.date.accessioned | 2016-03-04T16:34:27Z | |
dc.date.available | 2016-03-04T16:34:27Z | |
dc.date.issued | 2010 | en_ZA |
dc.description.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. | en_ZA |
dc.identifier.apacitation | Ravelomanana, 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/11427/17446 | en_ZA |
dc.identifier.chicagocitation | Ravelomanana, 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/11427/17446 | en_ZA |
dc.identifier.citation | Ravelomanana, 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.uri | http://hdl.handle.net/11427/17446 | |
dc.identifier.vancouvercitation | Ravelomanana 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/11427/17446 | en_ZA |
dc.language.iso | eng | en_ZA |
dc.publisher.department | Department of Mathematics and Applied Mathematics | en_ZA |
dc.publisher.faculty | Faculty of Science | en_ZA |
dc.publisher.institution | University of Cape Town | |
dc.subject.other | Mathematics | en_ZA |
dc.title | An elementary approach to some aspects of Heegaard Floer homology | en_ZA |
dc.type | Master Thesis | |
dc.type.qualificationlevel | Masters | |
dc.type.qualificationname | MSc | en_ZA |
uct.type.filetype | Text | |
uct.type.filetype | Image | |
uct.type.publication | Research | en_ZA |
uct.type.resource | Thesis | en_ZA |
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