Displaying similar documents to “A geometric description of differential cohomology”

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 geometry of a closed form

Marisa Fernández, Raúl Ibáñez, Manuel de León (1998)

Banach Center Publications

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It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on G 2 -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.

Vanishing of the first reduced cohomology with values in an L p -representation

Romain Tessera (2009)

Annales de l’institut Fourier

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We prove that the first reduced cohomology with values in a mixing L p -representation, 1 < p < ∞ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced ℓ p -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced L p -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes....

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...