Topology Seminar: Corrado De Concini (Rome)

(Joint work with C. Procesi and M.Vergne) Let G be a compact Lie group with Lie algebra g. Given a G-manifold M with a G equivariant one form w we consider the zeroes M^{0} of the corresponding moment map and define a map, called innitesimal index, of S[g*]^{G}-modules from the equivariant cohomology of M^{0} with compact support to the space of invariant distributions on g*. In the case in which G is a torus, N is a linear complex representation of G, M = T*N with tautological one form we are going to explain how this is used to compute the equivariant cohomology of M^{0} with compact support using certain spaces of polynomial which appear in approximation theory.