  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 gauge-independence is the non-triviality of
the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is
associated to the topological invariants of Mumford, Morita and Miller. Based
on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the
Workshop on String Theory, Trieste, 20-22 April 1994.
