All Questions
5 questions
10
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2
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Fukaya categories of hyperkahler reductions: general request for information
I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, see Nick Proudfoot's ...
9
votes
0
answers
629
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Orlov equivalence between Fukaya categories
In his famous paper https://arxiv.org/abs/math/0503632, Orlov proves the following theorem (for simplicity, let's just focus on the Calabi-Yau case)
Theorem(Orlov): Suppose that $W: \mathbb{A}^d \...
16
votes
2
answers
2k
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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 "...
20
votes
1
answer
4k
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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 ...
11
votes
1
answer
2k
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"Fourier-Mukai" functors for Fukaya categories?
I just skimmed a bit of this fresh-off-the-press paper on homological mirror symmetry for general type varieties.
One thing that intrigued me was statement (ii) of Conjecture 3.3. It suggests that, ...