Gilles Carron (2010)
Annales de l’institut Fourier
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When 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 harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.
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...
Nguyen Tien Zung (1996)
Compositio Mathematica
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Felipe Cano (1998)
Banach Center Publications
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Romain Tessera (2009)
Annales de l’institut Fourier
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We prove that the first reduced cohomology with values in a mixing -representation, , 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 -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes....
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...
Tomohiko Ishida (2012)
Annales de l’institut Fourier
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We study the cohomology of the group consisting of all -diffeomorphisms of the line, which are -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.