Let M be a compact Hamiltonian T−space, with finite fixed point set MT . An equivariant class is determined by its restriction
to MT , and to each fixed point p ∈ MT and generic component of the moment map, there corresponds a canonical class τp. For
a special class of Hamiltonian T−spaces, the value τp,q of τp at a fixed point q can be determined through an iterated interpolation
procedure, and we obtained a formula for τp,q as a sum over ascending chains from p to q. In general the number of such chains
is huge, and the main result of this paper is a procedure to reduce the number of relevant chains, through a systematic degeneration
of the interpolation direction. The resulting formula for τp,q resembles, via the localization formula, an integral over a space of
chains, and we prove that, for complex Grassmannians, τp,q can indeed be expressed as the integral of an equivariant form over a
smooth Schubert variety.