Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01jw827f828
DC FieldValueLanguage
dc.contributor.authorBai, Shaoyun
dc.contributor.otherMathematics Department
dc.date.accessioned2022-06-16T20:34:06Z-
dc.date.available2022-06-16T20:34:06Z-
dc.date.created2022-01-01
dc.date.issued2022
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01jw827f828-
dc.description.abstractIn 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.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherPrinceton, NJ : Princeton University
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu>catalog.princeton.edu</a>
dc.subjectequivariant transversality
dc.subjectFukaya categories
dc.subjectsymplectic topology
dc.subject.classificationMathematics
dc.titleInvariants from Equivariant Transversality in Symplectic Topology and Some Results on the Rouquier Dimension of Wrapped Fukaya Categories