Robert Wolak

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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 two(More)
In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. 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 fibrations we prove a de Rham type theorem for the basic intersection cohomology(More)
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 κμ (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)
We prove that the basic intersection cohomology IH ∗ p (M/F ), where F is the singular foliation determined by an isometric action of a Lie group G on the compact manifold M, is finite dimensional. This paper deals with an action Φ : G × M → M of a Lie group on a compact manifold preserving a riemannian metric on it. The orbits of this action define a(More)