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An elementary approach to some aspects of Heegaard Floer homology
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 t...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613142726475776 |
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| access_status_str | Open Access |
| author | Ravelomanana, Huygens Christian |
| author2 | Gay, David T. |
| author_browse | Gay, David T. Ravelomanana, Huygens Christian |
| author_facet | Gay, David T. Ravelomanana, Huygens Christian |
| author_sort | Ravelomanana, Huygens Christian |
| collection | Thesis |
| 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. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17446 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:26.417Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17446 An elementary approach to some aspects of Heegaard Floer homology Ravelomanana, Huygens Christian Gay, David T. Gilmour Christopher Mathematics 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. 2016-03-04T16:34:27Z 2016-03-04T16:34:27Z 2010 Master Thesis Masters MSc http://hdl.handle.net/11427/17446 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics Ravelomanana, Huygens Christian An elementary approach to some aspects of Heegaard Floer homology |
| thesis_degree_str | Master's |
| title | An elementary approach to some aspects of Heegaard Floer homology |
| title_full | An elementary approach to some aspects of Heegaard Floer homology |
| title_fullStr | An elementary approach to some aspects of Heegaard Floer homology |
| title_full_unstemmed | An elementary approach to some aspects of Heegaard Floer homology |
| title_short | An elementary approach to some aspects of Heegaard Floer homology |
| title_sort | elementary approach to some aspects of heegaard floer homology |
| topic | Mathematics |
| url | http://hdl.handle.net/11427/17446 |
| work_keys_str_mv | AT ravelomananahuygenschristian anelementaryapproachtosomeaspectsofheegaardfloerhomology AT ravelomananahuygenschristian elementaryapproachtosomeaspectsofheegaardfloerhomology |