Projections of self-similar sets with no separation condition

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, ω) a monotone symplectic manifold, admit categorifications as actions of the fundamental groupoid Π(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.