{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/17446"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/17446","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"An elementary approach to some aspects of Heegaard Floer homology","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.","abstract_html":"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_has_math":false,"creators":["Ravelomanana, Huygens Christian"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Gay, David T.","Gilmour Christopher"],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-24T01:33:45Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/17446","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Gay, David T.","Gilmour Christopher"]},{"key":"dc:creator","label":"Author","values":["Ravelomanana, Huygens Christian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-03-04T16:34:27Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-03-04T16:34:27Z"]},{"key":"dc:date.issued","label":"Date","values":["2010"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/17446"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["An elementary approach to some aspects of Heegaard Floer homology"]}]}],"canonical_facts":{"dc:contributor.advisor":["Gay, David T.","Gilmour Christopher"],"dc:creator":["Ravelomanana, Huygens Christian"],"dc:date.accessioned":["2016-03-04T16:34:27Z"],"dc:date.available":["2016-03-04T16:34:27Z"],"dc:date.issued":["2010"],"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."],"dc:identifier.uri":["http://hdl.handle.net/11427/17446"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["An elementary approach to some aspects of Heegaard Floer homology"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-24T01:33:45Z"}