There is the general principle to consider a classical invariant of a closed Riemannian
manifold M and to define its analog for the universal covering M taking the action of the …

We present the status of the Farrell–Jones Conjecture for algebraic K-theory for a group G
and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be …

This manuscript is not finished. Most of it is in nearly final form, whereas Chapters 8 and 25
are still under construction. Comments are very welcome. The Isomorphism Conjectures due …

Mathematische Annalen Page 1 DOI: 10.1007/s00208-004-0521-6 Math. Ann. 329, 597–621
(2004) Mathematische Annalen From acyclic groups to the Bass conjecture for amenable …

These notes are a compendium to a series of lectures concerning the topological aspects of
the Baum-Connes Conjecture—the left hand side of the equation K* G (EG)≅ K* top (C …

This paper is part of a series of articles on noncommutative geometry and conformal
geometry. In this paper, we reformulate the local index formula in conformal geometry in …

By deploying dense subalgebras of ℓ1 (G) we generalize the Bass conjecture in terms of
Connes' cyclic homology theory. In particular, we propose a stronger version of the ℓ1-Bass …

This note has its origins in talks discussing Bass' trace conjecture. After one such lecture (by
IC), R Geoghegan kindly mentioned his geometric perspective on the matter. Then, when …

The complex group algebra \BbbCG of a countable group G can be imbedded in the von
Neumann algebra NG of G. If G is torsion-free, and if P is a finitely generated projective …

In this paper we present the construction of explicit quasi-isomorphisms that compute the
cyclic homology and periodic cyclic homology of crossed-product algebras associated with …