  This paper gives a construction, using heat kernels, of differential forms on
the moduli space of metrised ribbon graphs, or equivalently on the moduli space
of Riemann surfaces with boundary. The construction depends on a manifold with
a bundle of Frobenius algebras, satisfying various conditions. These forms
satisfy gluing conditions which mean they form an open topological conformal
field theory, i.e. a kind of open string theory.
  If the integral of these forms converged, it would yield the purely quantum
part of the partition function of a Chern-Simons type gauge theory. Yang-Mills
theory on a four manifold arises as one of these Chern-Simons type gauge
theories.
