Residue formulas for push-forwards in equivariant cohomology - a symplectic approach

TL;DR

This paper develops residue formulas for push-forwards in equivariant cohomology by linking symplectic geometry with localization techniques, providing explicit formulas for classical homogeneous spaces.

Contribution

It introduces a symplectic approach to derive residue formulas for equivariant push-forwards, connecting localization theorems with geometric examples.

Findings

Residue formulas for push-forwards in equivariant cohomology are obtained.

The approach applies to classical Lie group homogeneous spaces.

Explicit examples include projective spaces and Grassmannians.

Abstract

The aim of this paper is to describe how to obtain residue-type formulas for push-forwards in equivariant cohomology, using the Jeffrey-Kirwan nonabelian localization theorem and the related result of Guillemin and Kalkman. This paper relates the description of equivariant push-forwards for homogeneous spaces of classical Lie groups with the action of the maximal torus with symplectic geometry, using the example of projective spaces and classical Grassmannians.