The search session has expired. Please query the service again.
We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly...
We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain
-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ϕ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H...
Un groupe localement compact a la propriété (T) de Kazhdan si la -cohomologie de tout -module hilbertien est nulle. Cette propriété de rigidité de la théorie des représentations de a trouvé des applications qui vont de la théorie ergodique à la théorie des graphes. Pendant près de 30 ans, les seuls exemples connus de groupes avec la propriété (T), provenaient des groupes algébriques simples sur les corps locaux, ou de leurs réseaux. La situation a radicalement changé ces dernières années :...
Let be an irreducible lattice in a product of simple groups. Assume that has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of in terms of the topology of the dual space of .We use this result to give a new proof for the triviality of the first cohomology group of with coefficients in a finite dimensional unitary representation.
We follow ideas going back to Gromov's seminal article [Publ. Math. IHES 56 (1982)] to show that the proportionality constant relating the simplicial volume and the volume of a closed, oriented, locally symmetric space M = Γ∖G/K of noncompact type is equal to the Gromov norm of the volume form in the continuous cohomology of G. The proportionality constant thus becomes easier to compute. Furthermore, this method also gives a simple proof of the proportionality principle for arbitrary manifolds.
Currently displaying 1 –
18 of
18