Thomas Schick: The trace on the K-theory of group C*-algebras
Abstract:
The canonical trace on the reduced C*-algebra of a discrete group
gives rise to a homomorphism from the K-theory of this C*-algebra
to the real numbers. This paper addresses the range of this
homomorphism. For torsion free groups, the Baum-Connes conjecture and
Atiyah's L2-index theorem implies that the range consists of the
integers. If the group is not torsion free, Baum and Connes
conjecture that the trace takes values in the rational numbers.
We give a direct and rather elementary proof that the range of this
trace for G x H and G x (F*H) coincide,
where F is a free group. This gives some evidence for the
conjectures and proves it in special cases.
Thomas Schick