Cyclic homology, C^*-algebras and the Strong Novikov Conjecture (10/96; revised 5/97), by Crichton Ogle

This is a further update of my K-theory archives posting Filtrations of Simplicial Functors, Topological K-theory and the Baum-Connes conjecture. We show the inclusion of the complex group algebra $\Bbb C[\pi]$ in the maximal $C^*$-algebra $C^*(\pi)$ induces an injection in algebraic cyclic homology. The has been substantially streamlined from the original version, and gap in the proof has been fixed. The result implies rational injectivity of the assembly map for the maximal $C^*$-algebra $C^*(\pi)$ for \underbar{all} discrete groups $\pi$.

The extensions to proving injectivity of the Baum-Connes assembly map in topological and algebraic $K$-theory, also announced in the first version, Filtrations of Simplicial Functors, Topological K-theory and the Baum-Connes conjecture, will be presented in separate postings.

This paper has been removed pending revision.


Crichton Ogle <ogle@math.osu.edu>