Q914197
type: Item
instance of: scholarly article
title: 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)
zbMATH Open document ID: 0701.57011
DOI: 10.5565/PUBLMAT_33389_06
author: Marta Macho Stadler
published in: Publicacions Matemàtiques
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/41084
review text: 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.
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 4149164
zbMATH Keywords: Baum-Connes conjecture
zbMATH Keywords: analytical K-theories
zbMATH Keywords: foliation
zbMATH Keywords: holonomy
zbMATH Keywords: classifying foliation
zbMATH Keywords: torus
Wikidata QID: Q123133358
reviewed by: Izu Vaisman
MaRDI profile type: Publication
label: 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)
description: scientific article; zbMATH DE number 4149164