English

On the localization formula in equivariant cohomology

Differential Geometry 2014-01-23 v3

Abstract

We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calculating the Gysin homomorphism in ordinary cohomology of an equivariant map. As an example, we recover a formula of Akyildiz-Carrell for the Gysin homomorphism of flag manifolds.

Keywords

Cite

@article{arxiv.math/0309068,
  title  = {On the localization formula in equivariant cohomology},
  author = {Andres Pedroza and Loring Tu},
  journal= {arXiv preprint arXiv:math/0309068},
  year   = {2014}
}

Comments

12 pages

R2 v1 2026-07-22T16:57:23.285Z