The moment map and equivariant cohomology with generalized coefficients

Paul-Emile Paradan (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Let M be a symplectic manifold acted on by a compact Lie group G in a Hamiltonian fashion, with proper moment map. In this situation we introduce a pushforward morphism from the equivariant cohomology of M to the space of G-invariant distributions on Lie(G), which gives rise to symplectic invariants, in particular the pushforward of the Liouville measure. For the study of this pushforward morphism we make an intensive use of equivariant forms with generalized coefficients.

Mots clés: Hamiltonian actions of compact Lie group; Moment map; Equivariant cohomology; Distribution; localization

Domaines: Géométrie symplectique [math.SG]

Paul-Emile Paradan. The moment map and equivariant cohomology with generalized coefficients. Topology, 2000, 39 (2), pp.401-444. ⟨10.1016/S0040-9383(99)00028-2⟩. ⟨hal-00773248⟩