homological mirror symmetry

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Examples

The mirror of \({\mathbf{CP}}^n\) is a Lefschetz fibration: attachments/Pasted%20image%2020220430185451.png

A full application of the usefulness of the Fukaya category: attachments/Pasted%20image%2020220430185646.png

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moment polytope in Unsorted/homological mirror symmetry
symplectic

See open string, closed string, Floer homology, quantum cohomology, symplectic cohomology, Lagrangian Floer cohomology, wrapped Floer cohomology, Fukaya category, homological mirror symmetry.
THH

Occurence in homological mirror symmetry:
Lagrangian Floer homology

Appears in homological mirror symmetry relating algebraic and symplectic geometry – the symplectic geometry side involves the geometry of Lagrangian submanifolds and their Floer homology groups. See the Fukaya category.
Fukaya category

Relation to homological mirror symmetry using Hochschild homology of derived categories: