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2005 | 53 | 4 | 429-440
Tytuł artykułu

Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations

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EN
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EN
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 example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy the Poincaré Duality. However, we recover the Poincaré Duality in the basic intersection cohomology. It is not accidental that the top-dimensional basic intersection cohomology groups of the example are isomorphic to either 0 or ℝ. We prove that this holds for any singular riemannian foliation of a compact connected manifold. As a corollary, we show that the tautness of the regular stratum of the singular riemannian foliation can be detected by the basic intersection cohomology.
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  • Departamento de Matemática Aplicada, Universidad del País Vasco, Alameda de Urquijo s/n, 48013 Bilbao, Spain
  • Fédération CNRS Nord-Pas-de-Calais FR 2956, UPRES-EA 2462 LML, Faculté Jean Perrin, Université d'Artois, Rue Jean Souvraz SP 18 62 307 Lens Cedex, France
autor
  • Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-ba53-4-8
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