Questions tagged [fukaya-category]

For questions about Fukaya categories (as introduced by Fukaya in 1993) and their structure; consider also related tags such as [floer-homology] or [lagrangian-submanifolds].

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Has anything precise been written about the Fukaya category and Lagrangian skeletons?

At some point in this past year, some Fukaya people I know got very excited about the Fukaya categories of symplectic manifolds with "Lagrangian skeletons." As I understand it, a Lagrangian ...
Ben Webster's user avatar
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19 votes
1 answer
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Hochschild (co)homology of Fukaya categories and (quantum) (co)homology

There is a conjecture of Kontsevich which states that Hochschild (co)homology of the Fukaya category of a compact symplectic manifold $X$ is the (co)homology of the manifold. (See page 18 of ...
Kevin H. Lin's user avatar
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17 votes
2 answers
3k views

Comparison between Hamiltonian Floer cohomology and Lagrangian Floer cohomology of the diagonal

Let X be a compact symplectic manifold with a form $\omega$. And $X \times X$ is equipped with the symplectic form $(\omega,-\omega)$. The diagonal $\Delta:X \mapsto X \times X$ is a Lagrangian ...
Daniel Pomerleano's user avatar
15 votes
2 answers
2k views

Deformation quantization and quantum cohomology (or Fukaya category) -- are they related?

Good afternoon. Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "...
Kevin H. Lin's user avatar
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9 votes
2 answers
2k views

Are Fukaya categories Calabi-Yau categories?

Let X be a compact symplectic manifold. There is an idea, I think probably originally due to Kontsevich, that we should be able to get Gromov-Witten invariants of X out of the Fukaya category of X. ...
Kevin H. Lin's user avatar
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