Semirigid Construction of Topological Supergravities

We show how to construct topological N = 1 and 2 supergravity theories from appropriately constrained N = 3 and 4 ghost plus matter systems. In particular N = 4 susy is not needed to obtain the N = 1 topological theory. We give a description of the relevant supermoduli spaces which must be integrated to obtain the amplitudes of these theories, as well as explicit formulas for the ingredients entering the integrands, in particular the various supercurrents with their inhomogeneous terms.