2026/06/10 by M. Abouzaid, K. Fukaya, Y. -G. Oh +2 · 1 voice
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.AT #math.DG
Given a finite collection of Lagrangian submanifolds \mathscr L in a compact symplectic manifold X, we construct a cyclic, filtered, strictly unital curved A∞ category \mathcal L and develop Floer theory of closed-open maps and open-closed maps. Using them, we prove that, whenever the map from the quantum cohomology of X to the Hochschild cohomology of the Fukaya category \mathcal L with objects \mathscr L is injective, the following consequences follow: (1) any other Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by \mathscr L, and (2) the Hochschild homology and cohomology of the Fukaya category are isomorphic to quantum cohomology. In the exact case a similar result was obtained in [Ab]. We also provide some applications.