Principe d'Oka, K-théorie et systèmes dynamiques non commutatifs.
We review the formulation and proof of the Baum-Connes conjecture for the dual of the quantum group of Woronowicz. As an illustration of this result we determine the K-groups of quantum automorphism groups of simple matrix algebras.
Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.