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For a riemannian foliation F on a closed manifold M , it is known that F is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form κ µ (relatively to a suitable riemannian metric µ) is zero (cf. [1]). In the transversally orientable case, tautness is equivalent to the non-vanishing of the top(More)
In recent years the graph of a foliation, an object which has been known for a long time, cf. 10], has known new interest. In fact there are two groupoids associated with a foliation, the homotopy groupoid and the holonomy groupoid, sometimes called the graph. It serves as a basis for the construction of the C-algebra associated to the foliation. Moreover,(More)
In the paper we introduce the notions of a singular fibration and a singular Seifert fi-bration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations defined by such fibra-tions we prove a de Rham type theorem for the basic intersection cohomology(More)
We study the cohomology properties of the singular foliation F determined by an action Φ : G× (M, µ) → (M, µ) where the abelian Lie group G preserves the riemannien metric µ on the compact manifold M. More precisely, we prove that the basic intersection cohomology IH * p (M/F) is finite dimensional and verifies the Poincaré Duality. This duality includes(More)
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an(More)
E-learning is widespread among pharmacists who take part in the continuing education courses. The fast development of e-learning platforms which provide educational courses has been noted. There is a need of standardization and validation of distance learning courses, especially as they have started to be recognized and accredited by continuing pharmacy(More)
To Nicolae Teleman on his 65th birthday. Abstract In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological(More)