{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/139233"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/139233","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Spectral Fukaya Categories for Liouville Manifolds","abstract":"This thesis constructs stable homotopy types underlying symplectic Floer homology, realizing a program proposed by Cohen, Jones and Segal twenty-five years ago. We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the moduli spaces of Floer trajectories are smooth and stably framed. We then develop a basic TQFT formalism, in the stable homotopy category, for producing operations on these Floer homotopy types from families of punctured Riemann surfaces. As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category.","abstract_html":"This thesis constructs stable homotopy types underlying symplectic Floer homology, realizing a program proposed by Cohen, Jones and Segal twenty-five years ago. We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the moduli spaces of Floer trajectories are smooth and stably framed. We then develop a basic TQFT formalism, in the stable homotopy category, for producing operations on these Floer homotopy types from families of punctured Riemann surfaces. As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category.","abstract_has_math":false,"creators":["Large, Tim"],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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We work in the setting of Liouville manifolds with a stable symplectic trivialization of their tangent bundles, where we prove that the moduli spaces of Floer trajectories are smooth and stably framed. We then develop a basic TQFT formalism, in the stable homotopy category, for producing operations on these Floer homotopy types from families of punctured Riemann surfaces. As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Spectral Fukaya Categories for Liouville Manifolds"]}]}],"canonical_facts":{"dc:contributor.advisor":["Seidel, Paul"],"dc:contributor.department":["Massachusetts Institute of Technology. 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As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/139233"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright MIT"],"dc:rights.uri":["http://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Spectral Fukaya Categories for Liouville Manifolds"],"dc:type":["Thesis"],"thesis:degree_name":["Doctoral","Doctor of Philosophy"]},"updated_at":"2026-07-22T22:22:13Z"}