In this paper we extend our correlation functions to the open/closed case.
This gives rise to actions of an open/closed version of the Sullivan PROP as
well as an action of the relevant moduli space. There are several unexpected
structures and conditions that arise in this extension which are forced upon us
by considering the open sector.

For string topology operations, one cannot just consider graphs, but has to
take punctures into account and one has to restrict the underlying Frobenius
algebras. In the moduli space, one first has to pass to a smaller moduli space
which is closed under open/closed duality and then consider covers in order to
account for the punctures.