Fukaya categories of hyperplane arrangements

To a simple polarized hyperplane arrangement (not necessarily cyclic) V, one can associate a stopped Liouville manifold (equivalently, a Liouville sector) (M(V),ξ), where M(V) is the complement of finitely many hyperplanes in Cd, obtained as the complexifications of the real hyperplanes in V. The Liouville structure on M(V) comes from a very affine embedding, and the stop ξ is determined by the polarization. In this article, we study the symplectic topology of (M(V), ξ). In particular, we prove that their partially wrapped Fukaya categories are generated by Lagrangian submanifolds associated to the bounded and feasible chambers of V. A computation of the Fukaya A∞-algebra of these Lagrangians then enables us to identify the partially wrapped Fukaya categories W(M(V), ξ) with the Gd m-equivariant hypertoric convolution algebras e B(V) associated to V. This confirms a conjecture of Lauda- Licata-Manion [29] and provides evidence for the general conjecture of Lekili-Segal [33] on the equivariant Fukaya categories of symplectic manifolds with Hamiltonian torus actions.