La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une variété fermée. (The Baum-Connes conjecture for a foliation without holonomy of codimension one in a closed manifold)
The Baum-Connes conjecture concerning the existence of an isomorphism between the topological and analytical K-theories of the space of leaves of a foliation \({\mathcal F}\) is reproven for the case where codim \({\mathcal F}=1\), and \({\mathcal F}\) is without holonomy. This result was first proven for the \(C^{\infty}\) case by \textit{T. Natsume} [Foliations, Proc. Symp., Tokyo 1983, Adv. Stud. Pure Math. 5, 15-27 (1985; Zbl 0658.57015)]. The present new proof holds also for \(C^ 0\)-foliations, and it is based on the construction of a classifying foliation \({\mathcal F}_ 0\) on a torus.
scientific article; zbMATH DE number 4149164