Displaying similar documents to “Vanishing of the first reduced cohomology with values in an L p -representation”

Rigidity and L 2 cohomology of hyperbolic manifolds

Gilles Carron (2010)

Annales de l’institut Fourier

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When X = Γ ∖ ℍ n is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of L 2 harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.

Second cohomology classes of the group of C 1 -flat diffeomorphisms

Tomohiko Ishida (2012)

Annales de l’institut Fourier

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We study the cohomology of the group consisting of all C ∞ -diffeomorphisms of the line, which are C 1 -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

A geometric description of differential cohomology

Ulrich Bunke, Matthias Kreck, Thomas Schick (2010)

Annales mathématiques Blaise Pascal

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In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [, , , ]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in []. There the starting point was Quillen’s cobordism description of singular...

On non-commutative twisting in étale and motivic cohomology

Jens Hornbostel, Guido Kings (2006)

Annales de l’institut Fourier

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This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 ( 𝒪 K [ 1 / S ] , H i ( X ¯ , ℚ p ( j ) ) ) , where X → Spec 𝒪 K [ 1 / S ] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H i ( X ¯ , ℤ p ( j ) ) . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.