Gerstenhaber and Batalin-Vilkovisky structures on Lagrangian intersections

Let M and N be Lagrangian submanifolds of a complex symplectic manifold S . We construct a Gerstenhaber algebra structure on $$mathcal{T}or_ast^{mathcal{O}_S}(mathcal{O}_M,mathcal{O}_N)$$ and a compatible Batalin–Vilkovisky module structure on $$mathcal{E}xt^ast_{mathcal{O}_S}(mathcal{O}_M,mathcal{O}_N)$$ . This gives rise to a de Rham type cohomology theory for Lagrangian intersections.