Several years ago Tom Bridgeland suggested that there should exist an interesting chain maps C_*(M_{g,n}) -> C_{*+2}(M_{g,n+1}) and he conjectured some applications of these maps to mirror symmetry. I shall present a precise definition of these maps using techniques from the theory of ribbon graphs, and discuss a conjectural statement about the homology of the total complex associated to the bicomplex obtained from these maps. Then I shall speculate (wildly) about applications to mirror symmetry.