| The homology of a 2-colored dioperad of decorated Riemann spheres with boundary, relevant to open-closed string field theory, is computed. An open-closed version of Voronov's cacti operad is defined and used to realize the algebraic; structure described by the 2-colored operad in an open-closed version of string topology. This 2-colored operad is then extended to a space of graphs modeling the full PROP of open-closed surfaces of arbitrary genus. Its application to open-closed string topology is studied. |
