Top dimensional group of the basic intersection cohomology for singular riemannian foliations

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dc.creatorPrieto, J. I. Royo
dc.creatorSaralegi-Aranguren, M.
dc.creatorWolak, R.
dc.date2005-05-31
dc.date2006-04-25
dc.date.accessioned2026-07-07T08:56:34Z
dc.date.available2026-07-07T08:56:34Z
dc.descriptionIt 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 its basic cohomology does not satisfy the Poincaré Duality property. We recover this property in the basic intersection cohomology. It is not by chance that the top dimensional basic intersection cohomology groups of the example are isomorphic to either 0 or $\mathbb{R}$. We prove in this Note that this holds for any singular riemannian foliation of a compact connected manifold. As a Corollary, we get that the tautness of the regular stratum of the singular riemannian foliation can be detected by the basic intersection cohomology.
dc.description11 pages. Accepted for publication in the Bulletin of the Polish Academy of Sciences
dc.identifierhttps://arxiv.org/abs/math/0505676
dc.identifierhttp://arxiv.org/abs/math/0505676
dc.identifierBulletin of the Polish Academy of Sciences 53(2005), 429-440.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146660
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.subject57R30
dc.titleTop dimensional group of the basic intersection cohomology for singular riemannian foliations
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