Max Karoubi

Representations approchees d'un groupe dans une algebre de banach

Let T be a continuous map from a compact group G to the group of invertible bounded linear operators on a Hilbert space H, the latter being endowed with the norm topology. If the norms ‖T(gh)-T(g)T(h)‖ are small enough (g,h ∈ G), we show that T is a small perturbation of some norm continuous representation of G on H.

Relations between algebraic K-theory and Hermitian K-theory

This paper is a continuation of [4] where we computed the homology groups with coefficients of the infinite orthogonal and symplectic groups of an algebraically closed field F of characteristic ≠2 and 0. Since we have also proved in [4] that these homology groups depend only on the characteristic of F (if it is different from 2), in order to deal with the case of characteristic zero, it is sufficient to compute this homology when F=C. More precisely, with the notations of [3] and [4], we shall prove the following statement:

TWISTED K-THEORY OLD AND NEW

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disproved the Baum-Connes Conjecture with coefficients.We present a

On the Baum–Connes conjecture in the real case

C^*

Algebraic and real K-theory of Real varieties

-algebra which is naturally associated to the

K-Theory and Noncommutative Geometry

ax+b

FORMES DIFFERENTIELLES NON COMMUTATIVES ET OPERATIONS DE STEENROD

-semigroup over

Equivariant K-theory of real vector spaces and real projective spaces

\mathbb N

Braiding of differential forms and homotopy types

. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which corresponds to addition. Its stabilization can be described as a crossed product of the algebra of continuous functions, vanishing at infinity, on the space of finite adeles for

K-theory for spherical space forms

\mathbb Q