Displaying similar documents to “On the Cech bicomplex associated with foliated structures”

Characteristic classes of subfoliations

Luis A. Cordero, X. Masa (1981)

Annales de l'institut Fourier

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This paper is devoted to define a characteristic homomorphism for a subfoliation ( F 1 , F 2 ) and to study its relation with the usual characteristic homomorphism for each foliation (as defined by Bott). Moreover, two applications are given: 1) the Yamato’s 2-codimensional foliation is shown to be no homotopic to F 2 in a (1,2)-codimensional subfoliation; 2) an obstruction to the existence of d everywhere independent and transverse infinitesimal transformations of a foliation F 2 is obtained, when...

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.

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...

The BIC of a singular foliation defined by an abelian group of isometries

Martintxo Saralegi-Aranguren, Robert Wolak (2006)

Annales Polonici Mathematici

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We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology ℍ * p ̅ ( M / ℱ ) is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group...

Natural liftings of foliations to the r -tangent bunde

Mikulski, Włodzimierz M.

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Let F be a p -dimensional foliation on an n -manifold M , and T r M the r -tangent bundle of M . The purpose of this paper is to present some reltionship between the foliation F and a natural lifting of F to the bundle T r M . Let L q r ( F ) ( q = 0 , 1 , ⋯ , r ) be a foliation on T r M projectable onto F and L q r = { L q r ( F ) } a natural lifting of foliations to T r M . The author proves the following theorem: Any natural lifting of foliations to the r -tangent bundle is equal to one of the liftings L 0 r , L 1 r , ⋯ , L n r . The exposition is clear and well organized. ...

Extending regular foliations

J. W. Smith (1969)

Annales de l'institut Fourier

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A p -dimensional foliation F on a differentiable manifold M is said to extend provided there exists a ( p + 1 ) -dimensional foliation F ' on M with F ⊂ F ' . Our main result asserts that if M and F extends over relatively compact subsets of M .