Residue formulas for push-forwards in equivariant cohomology: a symplectic approach (Q1729779)

For compact manifolds with an action of a torus, when the fixed point set of this action is finite, the push-forward (i.e. Gysin homomorphism -- Umkehrhomomorphismus) in equivariant cohomology (usually with coefficients in $\mathbb{C}$) is investigated. \par In a previous article the author described in terms of residue formulas the push-forward in equivariant cohomology of homogeneous spaces of classical Lie groups, with the action of the maximal torus. \par In this article it is shown that in the special case of classical Grassmannians, the aforementioned residue formulas can be deduced from results about nonabelian localization (proved by \textit{L. C. Jeffrey} and \textit{F. C. Kirwan} [Topology 34, No. 2, 291--327 (1995; Zbl 0833.55009)] and \textit{V. Guillemin} and \textit{J. Kalkman} [J. Reine Angew. Math. 470, 123--142 (1996; Zbl 0837.57028)]). It gives a natural geometric interpretation for the mentioned formulas.