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http://arks.princeton.edu/ark:/88435/dsp014j03d2400
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. |
URI: | http://arks.princeton.edu/ark:/88435/dsp014j03d2400 |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Mathematics, 1934-2024 |
Files in This Item:
File | Size | Format | |
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ZHANG-CHRISTOPHER-THESIS.pdf | 792 kB | Adobe PDF | Request a copy |
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