TOPOLOGICAL GRAVITY AND MODULI SPACE

We construct a theory of topological gravity in two dimensions, with a measure that is concentrated on constant curvature metrics. Following the insights of Ouvry, Stora and van Baal, we construct an equivalent cohomology theory, which we interpret as a cohomology theory for moduli space. We gauge fix our diffeomorphism-invariant action, following treatment in a previous article of the first author. We present nontrivial observables in this theory, and evaluate them in the weak coupling limit. These classical expressions are pushdowns of a curvature form (and its powers) on a line bundle over the universal curve. They bear a striking resemblance to Wolpert's expressions for the Mumford classes. © 1990.