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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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How should I think about B-fields?

Let me add a few words of explanation to Aaron's comment. Perturbative string theory is (at least at the level of caricature) concerned with describing small corrections to classical gravitational ph …
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6 votes

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

Yep. The connection I have in mind comes from recent work of Gukov & Witten: "Branes and Quantization". If you've got a symplectic manifold $M$, you can sometimes make the Kontsevich deformation of …
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