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Formules de localisation en cohomologie equivariante

Published online by Cambridge University Press:  04 December 2007

PAUL-EMILE PARADAN
PAUL-EMILE PARADAN
Affiliation:
Université Joseph Fourier, Department de Mathematiques, B.P. 74, 38402 Saint Martin d‘Hères
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Abstract

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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.

Keywords

equivariant cohomologyHamiltonian actionlocalizationmoment mapgeneralized equivariant forms.
Type
Research Article
Information
Compositio Mathematica , Volume 117 , Issue 3 , July 1999 , pp. 243 - 293
Copyright
© 1999 Kluwer Academic Publishers