Localization of Equivariant Cohomology for Compact and Non-compact Group Actions

Details Localization of Equivariant Cohomology for Compact and Non-compact Group Actions Localization of Equivariant Cohomology for Compact and Non-compact Group Actions

2005-02-09

arxiv.org/abs/math/0502190v2

Mathematics

Symplectic Geometry

30 pages, 4 figures

Scientific paper

We give a brief introduction to the Berline-Vergne localization formula for the finite-dimensional setting and indicate how the Duistermaat-Heckman formula is derived from it. We consider applications of the localization formula when it is specialized to a maximal dimensional co-adjoint orbit. In particular, the case when the co-adjoint orbit is a quotient $G/T$ of a connected Lie group $G$ modulo a maximal torus $T$ is analyzed in detail. We describe also a generalization of the localization formula to non-compact group actions.

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