Contenu
Le Problème de Cousin basique sur le groupe de Heisenberg réel
Toussaint SOHOU
Laboratoire: Mathématiques Fondamentales
U.F.R: Mathématiques et Informatique
Université Félix Houphout Boigny,
22 BP 582 Abidjan 22, Côte d’ Ivoire
Mathematics Subject Classification: (2010) Primary 55N30, 53C12; Secondary 32M05
Key words: Cohomology spaces. Foliations. Heisenberg group.
Abstract:
Let F = ℂ3, B = ∕Γ with the real three dimensional Heisenberg
group and Γ = π1 the fundamental group of B. Let be the transversely
holomorphic three codimensional foliation on the manifold M = (F ×)∕Γ
obtained by the suspension of a representation of Γ in Aut(F) the group of
automorphisms of F.
We want to compute the cohomology spaces H*(M,) where is the sheaf of
germs of basic holomorphic functions of the foliated manifold (M,), especially
H1(M,) which contains the obstructions to the resolution of the basic
additive Cousin problem.