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Title: Invariants from Equivariant Transversality in Symplectic Topology and Some Results on the Rouquier Dimension of Wrapped Fukaya Categories
Authors: Bai, Shaoyun
Advisors: Pardon, John
Contributors: Mathematics Department
Keywords: equivariant transversality
Fukaya categories
symplectic topology
Subjects: Mathematics
Issue Date: 2022
Publisher: Princeton, NJ : Princeton University
Abstract: In this thesis, we construct several invariants in low-dimensional topology and symplectic topology, including a symplectic definition of generalized Casson invariants, an extension of Taubes' Gromov invariants to symplectic Calabi-Yau threefolds, and integer-valued genus 0 Gromov--Witten type invariants for general compact symplectic manifolds, based on solutions to various equivariant transversality problems in symplectic topology. In a different direction, we also study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds to obtain applications in algebraic geometry and symplectic geometry.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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