A FUNCTIONAL AND LAGRANGIAN FORMULATION OF TWO DIMENSIONAL TOPOLOGICAL GRAVITY

We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant observables are shown to be globally defined forms on moduli space. The potential obstruction to their gaugeindependence is the non-triviality of the line bundle on moduli space Lx, whose first Chern-class is associated to the topological invariants of Mumford, Morita and Miller.