Three-dimensional topology and Verlinde formulas

We study the properties of the gauge invariant observables of the three-dimensional Chern-Simons field theory; it is shown that the algebra structure determined by the observables is isomorphic with the fusion rules of two-dimensional conformal theories. In the colour state space of the link components, a projective representation of the modular group is defined. The relations satisfied by the S matrix of the conformal models admit an interpretation in terms of three-dimensional topology; we describe the topological origin of these relations.