{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/60197"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/60197","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The Seiberg-Witten equations on a surface times a circle","abstract":"In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten monopoles. In the case where the monopoles are not Morse-Bott regular, I explicitly perturb the equations to obtain such a situation and thus find a candidate for the chain complex that calculates the Seiberg-Witten Floer homology groups.","abstract_html":"In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten monopoles. In the case where the monopoles are not Morse-Bott regular, I explicitly perturb the equations to obtain such a situation and thus find a candidate for the chain complex that calculates the Seiberg-Witten Floer homology groups.","abstract_has_math":false,"creators":["Lopes, William Manuel"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Tomasz S. Mrowka."],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:21:02Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/60197","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Tomasz S. Mrowka."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:creator","label":"Author","values":["Lopes, William Manuel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2010-12-06T17:36:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2010-12-06T17:36:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2010"]},{"key":"dc:publisher","label":"Institution","values":["Massachusetts Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/60197"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 63)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten monopoles. In the case where the monopoles are not Morse-Bott regular, I explicitly perturb the equations to obtain such a situation and thus find a candidate for the chain complex that calculates the Seiberg-Witten Floer homology groups."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["The Seiberg-Witten equations on a surface times a circle"]}]}],"canonical_facts":{"dc:contributor.advisor":["Tomasz S. Mrowka."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Lopes, William Manuel"],"dc:date.accessioned":["2010-12-06T17:36:45Z"],"dc:date.available":["2010-12-06T17:36:45Z"],"dc:date.issued":["2010"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 63)."],"dc:description.abstract":["In this thesis I study the Seiberg-Witten equations on the product of a genus g surface [Sigma] and a circle. I exploit S1 invariance to reduce to the vortex equations on [Sigma] and thus completely describe the Seiberg-Witten monopoles. In the case where the monopoles are not Morse-Bott regular, I explicitly perturb the equations to obtain such a situation and thus find a candidate for the chain complex that calculates the Seiberg-Witten Floer homology groups."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/60197"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["The Seiberg-Witten equations on a surface times a circle"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:02Z"}