AFRICA MATHEMATICS ANNALS

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: (MSC 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.