In [C2], Baum-Connes state a conjecture for the K-theory of C*-algebras of foliations. This conjecture has been proved by T. Natsume [N2] for C∞-codimension one foliations without holonomy on a closed manifold. We propose here another proof of the conjecture for this class of foliations, more geometric and based on the existence of the Thom isomorphism, proved by A. Connes in [C3]. The advantage of this approach is that the result will be valid for all C0-foliations.
@article{urn:eudml:doc:41084,
title = {La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une vari\'et\'e ferm\'ee.},
journal = {Publicacions Matem\`atiques},
volume = {33},
year = {1989},
pages = {445-457},
mrnumber = {MR1038483},
zbl = {0701.57011},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41084}
}
Macho Stadler, Marta. La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une variété fermée.. Publicacions Matemàtiques, Tome 33 (1989) pp. 445-457. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41084/