Degenerate Chern-Weil Theory and Equivariant Cohomology
Differential Geometry
2007-05-23 v2 Algebraic Topology
Symplectic Geometry
Abstract
We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an equivariant closed form within its cohomological class to a form more suitable to yield localization results. This work is motivated by our work on reproving wall crossing formulas in Seiberg-Witten theory, where the Lie group is the circle. As applications, we derive two localization formulas of Kalkman type for G = SU(2) or SO(3)-actions on compact manifolds with boundary. One of the formulas is then used to yield a very simple proof of a localization formula due to Jeffrey-Kirwan in the case of G = SU(2) or SO(3).
Keywords
Cite
@article{arxiv.math/9804135,
title = {Degenerate Chern-Weil Theory and Equivariant Cohomology},
author = {Huai-Dong Cao and Jian Zhou},
journal= {arXiv preprint arXiv:math/9804135},
year = {2007}
}
Comments
23 pages, AMSLaTex