Recursion Relations in Semirigid Topological Gravity

A field theoretical realization of topological gravity is discussed in the semirigid geometry context. In particular, its topological nature is given by the relation between de Rham cohomology on the moduli space and equivariant BRST cohomology on the Hilbert space and the fact that all but one of the physical operators are BRST exact. The puncture equation and the dilaton equation of pure topological gravity are reproduced, following Ref. 1.