Formules de localisation en cohomologie équivariante

Paul-Emile Paradan (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: equivariant cohomology; Hamiltonian action; localization; moment map; generalized equivariant forms

Domaines: Géométrie symplectique [math.SG]

Paul-Emile Paradan. Formules de localisation en cohomologie équivariante. Compositio Mathematica, 1999, 117 (3), pp.243-293. ⟨10.1023/A:1000602914188⟩. ⟨hal-00773247⟩