{Descendants constructed from matter field in 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(not necessarily conformal) can be constructed from matter fields alone (without metric fields and \hbox {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: $K^i(\sigma _i (\Phi _1), \Phi _2)=K^0(\Phi _1, \Phi _2)$),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).