Displaying similar documents to “The BIC of a singular foliation defined by an abelian group of isometries”

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

José Ignacio Royo Prieto, Martintxo Saralegi-Aranguren, Robert Wolak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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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...

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

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This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension ≤ 4 and ≥ 11 . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real...

Algebras of the cohomology operations in some cohomology theories

A. Jankowski

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Contents0. Introduction............................................................................................................................................. 51. Preliminaries.......................................................................................................................................... 62. Generalized cohomology theories with a coefficient group Z p .............................................. 83. Cohomology theory BP* ( , Z p )........................................................................................................

On the Cech bicomplex associated with foliated structures

Haruo Kitahara, Shinsuke Yorozu (1978)

Annales de l'institut Fourier

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For a codimension q foliation on a manifold, η × ( d η ) q defines the Godbillon-Vey class. We show that η itself defines a certain cohomology class, via the Cech bicomplex.

Localization of basic characteristic classes

Dirk Töben (2014)

Annales de l’institut Fourier

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We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold M is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type...

Cutting description of trivial 1-cohomology

Andrzej Czarnecki (2014)

Annales Polonici Mathematici

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A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.

BGG resolutions via configuration spaces

Michael Falk, Vadim Schechtman, Alexander Varchenko (2014)

Journal de l’École polytechnique — Mathématiques

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We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the 𝔰𝔩 2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.

Double complexes and vanishing of Novikov cohomology

Hüttemann, Thomas (2011)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15. We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new...

Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

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Each Lie algebra ℱ of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ℱ ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k ≥ 0 there exists a foliated compact manifold with E k ( ℱ ) infinite dimensional.