Fukaya category

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Fukaya category

Categorifies Lagrangian Floer homology. attachments/Pasted%20image%2020220430184718.png attachments/Pasted%20image%2020220430184821.png

A warning about the A_infty products:

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Idea: attachments/Pasted%20image%2020220424200451.png

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Relation to homological mirror symmetry using Hochschild homology of derived categories: attachments/Pasted%20image%2020220424170014.png

Description of a certain wrapped Fukaya category \({\mathcal{O}}\): take the objects to be Lagrangian embedded curves, the morphisms are the graded abelian groups \(\hom_{\mathcal{O}}\coloneqq\qty{\bigoplus_{L_0 \pitchfork L_1} {\mathbf{Z}}/2{\mathbf{Z}}, {{\partial}}}\) wher \({{\partial}}\) is given by counting holomorphic strips, localize along small isotopies.

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Wrapped Fukaya

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