  We study the equivariant cohomology of a class of multi-field topological LG
models, and find that such systems carry intrinsic information about
$W$-gravity. As a result, we can construct the gravitational chiral ring in
terms of LG polynomials. We find, in particular, that the spectrum of such
theories seems to be richer than so far expected. We also briefly discuss the
BRST operator for non-linear topological $W$-gravity.

High Energy Physics - Theory