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.
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