79 research outputs found
The Chern-Connes character is not rationally injective
We show that the Chern-Connes character from Kasparov's bivariant K-theory to
bivariant local cyclic cohomology is not always rationally injective.
Counterexamples are provided by the reduced group -algebras of
word-hyperbolic groups with Kazhdan's property (T). The proof makes essential
use of Skandalis' work on K-nuclearity and of Lafforgue's recent demonstration
of the Baum-Connes conjecture with coefficients for word-hyperbolic groups
New holomorphically closed subalgebras of -algebras of hyperbolic groups
We construct dense, unconditional subalgebras of the reduced group
-algebra of a word-hyperbolic group, which are closed under holomorphic
functional calculus and possess many bounded traces. Applications to the cyclic
cohomology of group -algebras and to delocalized -invariants of
negatively curved manifolds are given
Local cyclic homology of group Banach algebras of "non-positively curved" discrete groups
We calculate the local cyclic homology of group Banach-algebras of discrete
groups acting properly, isometrically and cocompactly on a CAT(0)-space.Comment: 33 page
Entire cyclic homology of continuous trace algebras
A central result here is the computation of the entire cyclic homology of
canonical smooth subalgebras of stable continuous trace C*-algebras having
smooth manifolds M as their spectrum. More precisely, the entire cyclic
homology is shown to be canonically isomorphic to the continuous periodic
cyclic homology for these algebras. By an earlier result of the authors, one
concludes that the entire cyclic homology of the algebra is canonically
isomorphic to the twisted de Rham cohomology of M.Comment: 7 pages, Latex2e, minor typos correcte
Superpotential algebras and manifolds
In this paper we study a special class of Calabi-Yau algebras (in the sense
of Ginzburg): those arising as the fundamental group algebras of acyclic
manifolds. Motivated partly by the usefulness of `superpotential descriptions'
in motivic Donaldson-Thomas theory, we investigate the question of whether
these algebras admit superpotential presentations. We establish that the
fundamental group algebras of a wide class of acyclic manifolds, including all
hyperbolic manifolds, do not admit such descriptions, disproving Ginzburg's
conjecture regarding them. We also describe a class of manifolds that do admit
such descriptions, and discuss a little their motivic Donaldson-Thomas theory.
Finally, some links with topological field theory are described.Comment: 31 pages, 2 figures, final version. Thanks to M. Kontsevich, V.
Ginzburg, M, Van den Bergh and B. Keller for helpful comments and
corrections. I've added some examples e.g. Klein bottl
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