A suitable quiver determines a 3CY category with a distinguished heart. We show how using the counting invariants of this category we can construct an infinite-dimensional Frobenius type structure on the space of stability conditions supported on this heart, with some convergence properties. We prove that under (restrictive) conditions this can be pulled back to a genuine family of Frobenius manifold structures. Our main example is that of A_n quivers. In this case we can also understand what happens in our construction when we mutate the quiver: we get a different branch of the same semisimple Frobenius manifold. Joint with A. Barbieri and T. Sutherland.