. K T ] 4 A ug 1 99 9 The trace on the K - theory of group C ∗ - algebras
نویسنده
چکیده
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 L-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 if H G then the range of this trace for the amalgamated free product G ∗H (H × F ) and for G coincide, where F is a free group. This gives some evidence for the conjectures and proves it in special cases. MSC: 19K (primary); 19K14, 19K35, 19K56 (secondary)
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