The relation between the Baum-Connes Conjecture and the Trace Conjecture

By W. Lück. 2002

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Subalgebras of simple AF-algebras (2018, methodology): “A result of Higson and Kasparov in [39] shows G satisfies the Baum-Connes conjecture, and hence a result of Lück in [52] shows that if τC∗r(G) denote the canonical trace on C ∗ r(G), then for all projections p ∈ Cr(G) ⊗ K, (τC∗r(G) ⊗ TrK)(p) ∈ Q.”
Survey on Classifying Spaces for Families of Subgroups (2003, unknown): “Rational computations of equivariant (co-)-homology groups are possible in general using Chern characters for discrete groups and proper G-CW -complexes (see [50], [51], [52]).”
The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, background): “Equivariant Chern Characters Equivariant Chern characters have been studied in [201] and [203] and allow to compute equivariant homology theories for proper G-CW-complexes.”
On the Farrell–Jones Conjecture and its applications (2007, methodology): “The Kadison Conjecture follows from the Baum-Connes Conjecture (as explained for instance in [42], [45, 1.”
L 2 -index theorems, KK-theory, and connections (2005, background): “2 Atiyah’s L(2)-index Now we are in the situation to give a proof of one of the goals of this paper: Atiyah’s L(2)-index, and its center valued generalization considered by Lück in [10] can be obtained from the index an operator defines in the K-theory of a corresponding C∗-algebra.”