Fusion potentials for Gk and handle squashing

Using Chern-Simons gauge theory, we show that the fusion ring of the conformal field theory Gk (G any Lie algebra) is isomorphic to P[u]/(∇V) where (∇V) is the ideal generated by conditions ∇V=0. We explicitly construct V for all Gk. We also derive a residue-like formula for the correlation functions in the Chern-Simons theory thus providing an RCFT version of the residue formula for the topological Landau-Ginzburg model. An operator that acts like a measure in this residue formula has the interpretation of a handle-squashing operator and explicit formulae for this operator are given. (orig.)