Degenerate Chern-Weil Theory and Equivariant Cohomology

Details Degenerate Chern-Weil Theory and Equivariant Cohomology Degenerate Chern-Weil Theory and Equivariant Cohomology

1998-04-29

arxiv.org/abs/math/9804135v2

Mathematics

Differential Geometry

23 pages, AMSLaTex

Scientific paper

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).

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