CATEGORIFICATION OF SEIDEL'S REPRESENTATION

Two natural symplectic constructions, the Lagrangian suspension and Seidel's quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M,omega) a monotone symplectic manifold, admit categorifications as actions of the fundamental groupoid Pi(Ham(M)) on a cobordism category recently introduced in [BC14] and, respectively, on a monotone variant of the derived Fukaya category. We show that the functor constructed in [BC14] that maps the cobordism category to the derived Fukaya category is equivariant with respect to these actions.