Exotic crossed products and the Baum–Connes conjecture (D02)

关于C*-代数上群作用的交叉积K-理论的Baum-Connes猜想是非对易几何的中心问题之一。这个猜想适用于大类群，并在数学的其他领域有重要的应用。然而，有些群的猜想不是真的，在这个项目中，我们研究了由于Baum，Guentner和Willett的猜想的一个新的公式，它避免了经典猜想的已知反例。这涉及到新的奇异交叉积函子，它们不同于经典的极大或约化交叉积。

The Baum–Connes conjecture on the K-theory of crossed products by group actions on C*-algebras is one of the central problems in noncommutative geometry. The conjecture holds for large classes of groups and has important applications in other areas of mathematics. However, there are groups for which the conjecture fails to be true and in this project we study a new formulation of the conjecture due to Baum, Guentner and Willett which avoids the known counterexamples for the classical one. This involves new exotic crossed product functors which differ from the classical maximal or reduced crossed products.