Feuilletages en surfaces, cycles évanouissants et variétés de Poisson.
L2-Cohomologie des espaces stratifiés.
Lemme de Moser feuilleté et clasifications des variétés de Poisson régulières.
Regular Poisson structures with fixed characteristic foliation F are described by means of foliated symplectic forms. Associated to each of these structures, there is a class in the second group of foliated cohomology H(F). Using a foliated version of Moser's lemma, we study the isotopy classes of these structures in relation with their cohomology class. Explicit examples, with dim F = 2, are described.
Groupoïdes riemanniens.
We propose a definition of a Riemannian groupoid, and we show that the Stefan foliation that it induces is a Riemannian (singular) foliation. We also prove that the homotopy groupoid of a Riemannian (regular) foliation is a Riemannian groupoid.
Page 1