Displaying similar documents to “Multivalued Lyapunov functions for homeomorphisms of the 2-torus”

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...

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.

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...

Nash cohomology of smooth manifolds

W. Kucharz (2005)

Annales Polonici Mathematici

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A Nash cohomology class on a compact Nash manifold is a mod 2 cohomology class whose Poincaré dual homology class can be represented by a Nash subset. We find a canonical way to define Nash cohomology classes on an arbitrary compact smooth manifold M. Then the Nash cohomology ring of M is compared to the ring of algebraic cohomology classes on algebraic models of M. This is related to three conjectures concerning algebraic cohomology classes.

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...