  By studying spaces of flow graphs in a closed oriented manifold, we construct
operations on its cohomology, parametrized by the homology of the moduli spaces
of compact Riemann surfaces with boundary marked points. We show that the
operations satisfy the gluing axiom of an open homological conformal field
theory. This complements previous constructions due to R. Cohen et al., K.
Costello and M. Kontsevich and is also the Morse theoretic counterpart to a
conjectural construction of operations on the Lagrangian Floer homology of the
zero section of a cotangent bundle, obtained by studying uncompactified moduli
spaces of higher genus pseudoholomorphic curves.
