## Introduction to non commutative differential geometry.(English)Zbl 0564.58002

Arbeitstag. Bonn 1984, Proc. Meet. Max-Planck-Inst. Math., Bonn 1984, Lect. Notes Math. 1111, 3-16 (1985).
[For the entire collection see Zbl 0547.00007.]
The author announces a series of papers devoted to the study of spaces such as: the space of leaves of a foliation, the dual space of a non- Abelian discrete (or Lie) group or the orbit space of the action of a discrete (or Lie) group on a manifold. The subject of this paper is: the construction of de Rham homology for the above spaces and its application to the K-theory and index theory. The first two papers of this series will appear soon in the IHES Publications.
Reviewer: P.Walczak

### MSC:

 58A99 General theory of differentiable manifolds 57R30 Foliations in differential topology; geometric theory 58J20 Index theory and related fixed-point theorems on manifolds 58A12 de Rham theory in global analysis 58A25 Currents in global analysis 55N15 Topological $$K$$-theory

Zbl 0547.00007