ON THE LANDAU-GINZBURG REALIZATION OF TOPOLOGICAL GRAVITIES

We study the equivariant cohomology of a class of multi-field topologi cal Landau-Ginzburg models, and find that such systems carry intrinsic information about W-gravity. As a result, we can construct the gravit ational chiral ring in terms of LG polynomials. We find, in particular , that the spectrum of such theories seems to be richer than so far ex pected. We also briefly discuss the BRST operator for non-linear topol ogical W-gravity.