Abstract
In this paper, we develop a method of localization in equivariant cohomology based on the notion of partition of unity cohomology. We apply this method in two cases. In the first case, this method gives a refinement of the localization of Atiyah–Bott and Berline–Vergne (in the frame given by Bismut). After, we consider the Hamiltonian action of a torus, and we realise, following the idea of Witten, the localization on the critical points of the square of the moment map.
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Paradan, PE. Formules de localisation en cohomologie equivariante. Compositio Mathematica 117, 243–293 (1999). https://doi.org/10.1023/A:1000602914188
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DOI: https://doi.org/10.1023/A:1000602914188