Homological mirror symmetry for noncommutative two-tori

Let ${\cal C}^A$ be the cyclic $A_\infty$-category obtained from Fukaya's $A_\infty$-category $(V^F,\eta^F,{\frak m}^F)$ by suspension, and let ${\cal C}^B$ be the cyclic $A_\infty$-category obtained by suspension from the cyclic DG category $(V,\eta,d,\varphi)$. Homological mirror symmetry for noncommutative two-tori. The cyclic $A_\infty$-categories ${\cal C}^A$ and ${\cal C}^B$ are homotopic to each other. This is the paper's noncommutative-torus formulation of homological mirror symmetry, identifying the A-model Fukaya-side structure with the B-model DG-category structure. The supplied text does not establish the claim as a theorem or give evidence resolving its conjectural status.