S.M.A. Balea:Cohomologies on the foliated Riemannian manifolds, p.3-10

Abstract:

The summary of this text might be helpful. We extend the de Rham theory of cohomology from a restricted context -- the classical real cohomology of a manifold -- to the cohomologies of the foliated Riemannian manifolds -- the basic and the foliated cohomology. The cohomologies of the manifolds with these coefficients sheaves can be calculated with de Rham type theorems. We obtain relations between coefficients in the sheaf of foliated Riemannian manifold and the cohomology with coefficients in the real sheaf of germs of foliated functions.

Key Words: Foliated Riemannian manifolds, cohomology, basic functions, basic cohomology, foliated functions, foliated cohomology, de Rham complex.

2000 Mathematics Subject Classification: Primary: 53B20,
Secondary 53C22, 53C23, 14J70.

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