Descendants constructed from matter field in topological Landau-Ginzburg theories coupled to topological gravity

It is argued that gravitational descendants in the theory of topological gravity coupled to topological Landau-Ginzburg theory can be constructed from matter fields alone (without metric fields and ghosts).In this sense topological gravity is ”induced”. We discuss the mechanism of this effect(that turns out to be connected with K.Saito’s higher residue pairing: K(σi(Φ1),Φ2) = K(Φ1,Φ2) , and demonstrate how it works in a simplest nontrivial example: correlator on a sphere with four marked points . We also discuss some results on k-point correlators on a sphere. From the idea of ”induced” topological gravity it follows that the theory of ”pure” topological gravity (without topological matter) is equivalent to the ”trivial” Landau-Ginzburg theory (with quadratic superpotential).