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Title: Fukaya Categories and Intersection Numbers
Authors: Zhang, Christopher
Advisors: Bottman, Nathaniel
Horton, Henry
Department: Mathematics
Class Year: 2018
Abstract: We give an introductory survey of Floer homology and Fukaya categories assuming only basic symplectic geometry. The survey is meant to be targeted at a lower level than Auroux’s survey [3]. We say very little about the analytical details involved in Fukaya categories and move quickly to discuss the algebraic side. We show an application of these algebraic techniques by proving a theorem by Keating about symplectic Dehn twists [14]. This theorem is a generalization of the theorem that if two curves α, β have minimal geometric intersection number ≥ 2, then the Dehn twists τα, τβ generate a free subgroup of the mapping class group.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

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