Displaying similar documents to “d...-Cohomology of Lagrangian Foliations.”

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...

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...

Bilipschitz invariance of the first transverse characteristic map

Michel Hilsum (2012)

Banach Center Publications

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Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.

Lagrangian holonomy ; characteristic elements of a lagrangian foliation

Carlos Currás-Bosch, Pierre Molino (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let ℒ be a lagrangian foliation on a symplectic manifold ( M 2 n , ω ) . The characteristic elements of such a foliation associated to a lagrangian total transversal are obtained; they are a generalisation of the characteristic elements given by J.J. Duistermaat [5]. This technique is applied to give a classification of the germs of lagrangian foliation along a compact leaf. Several examples of classification are given.

On G-foliations

Robert Wolak (1985)

Annales Polonici Mathematici

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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...

Multivalued Lyapunov functions for homeomorphisms of the 2-torus

Patrice Le Calvez (2006)

Fundamenta Mathematicae

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Let F be a homeomorphism of 𝕋² = ℝ²/ℤ² isotopic to the identity and f a lift to the universal covering space ℝ². We suppose that κ ∈ H¹(𝕋²,ℝ) is a cohomology class which is positive on the rotation set of f. We prove the existence of a smooth Lyapunov function of f whose derivative lifts a non-vanishing smooth closed form on 𝕋² whose cohomology class is κ.