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Banach $$KK$$-theory and the Baum-Connes conjecture. (English) Zbl 1030.19002
Casacuberta, Carles (ed.) et al., 3rd European congress of mathematics (ECM), Barcelona, Spain, July 10-14, 2000. Volume II. Basel: Birkhäuser. Prog. Math. 202, 34-46 (2001).
This paper discusses progress on the Baum-Connes conjecture. The emphasis is on the motivation for and implementation of the ideas of the author [Invent. Math. 149, 1-95 (2002; Zbl 1084.19003)] for using Banach $$KK$$-theory to attack the conjecture. This clearly written, interesting paper includes some comments on the likely reach and limitations of the author’s techniques.
For the entire collection see [Zbl 0972.00032].
##### MSC:
 19K35 Kasparov theory ($$KK$$-theory) 58J22 Exotic index theories on manifolds 46L80 $$K$$-theory and operator algebras (including cyclic theory) 46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
##### Keywords:
Baum-Connes conjecture; Banach $$KK$$-theory
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