Conformal boundary conditions and three-dimensional topological field theory

We present a general construction of all correlation functions of a two-dim ensional rational conformal field theory, for an arbitrary number of bulk a nd boundary fields and arbitrary topologies; The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manif old. The amplitudes constructed this way can be shown to be modular invaria nt and to obey the correct factorization rules.