5
votes
2answers
901 views

Hochschild homology of Fukaya category in mirror symmetry

Hi Can one explain to me what is the Hochschild homology of Fukaya category? I mean the definition. You can use the notations of FOOO (Fukaya-Oh-Ono-Ohta) if it helps you to explain easier. I know ...
7
votes
1answer
1k views

“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, ...
14
votes
4answers
3k views

Is the Fukaya category “defined”?

Sometimes people say that the Fukaya category is "not yet defined" in general. What is meant by such a statement? (If it simplifies things, let's just stick with Fukaya categories of compact ...