Spectral Fukaya Categories for Liouville Manifolds

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Author(s)
Large, Tim
Advisor(s)
Seidel, Paul
Date Issued
June 2021
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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