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|Title:||Fukaya Categories and Intersection Numbers|
|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 . 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 . 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|
|Appears in Collections:||Mathematics, 1934-2020|
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