Paul-Emile Paradan

The moment map and equivariant cohomology with generalized coefficients

Abstract 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 P : H ∗ G (M)→ M −∞ ( g ∗ ) G , from the equivariant cohomology of M to the space of G-invariant distributions on 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.

Admissible coadjoint orbits for compact Lie groups

The purpose of the present paper is a careful study of the quantization of admissible coadjoint orbits for compact Lie groups.

Wall-crossing formulas in Hamiltonian geometry

In this article, we study the local invariants associated to the Hamiltonian action of a compact torus. Our main results are wall-crossing formulas between invariants attached to adjacent connected components of regular values of the moment map.