Qin's dual-torus Fukaya-category equivalence conjecture

Let T=V/ΛT=V/\Lambda be a torus equipped with complexified symplectic form B+iωB+i\omega, and let

T=V/ΛT^\vee=V^\vee/\Lambda^\vee

be its dual torus equipped with (B+iω)1(B+i\omega)^{-1}.

Qin's dual-torus Fukaya-category conjecture. The Fukaya category of (T,B+iω)(T,B+i\omega) should be equivalent to the Fukaya category of its dual (T,(B+iω)1)(T^\vee,(B+i\omega)^{-1}).

This claim expresses the categorical equivalence expected from mirror symmetry for dual tori. In the surrounding discussion, the equivalence is motivated by the identification of the twisted doubling tori up to a B-field twist; the source does not state that the conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Yingdi Qin, “Coisotropic branes on tori and Homological mirror symmetry”, arXiv:2207.10647 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.