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Degenerate Chern-Weil Theory and Equivariant Cohomology - MaRDI portal

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Degenerate Chern-Weil Theory and Equivariant Cohomology

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Publication:6500883

arXivmath/9804135MaRDI QIDQ6500883

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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).





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