Arthur Bartels: K-theory of group rings (Lecture 4)

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields.

The Farrell-Jones Conjecture predicts that the K-theory of group rings RG can be computed in terms of K-theory of group rings RV where V varies over the collection of virtually cyclic subgroups of G.

In these talks I will discuss this conjecture, its formulation and methods of proof. Controlled algebra provides a bridge between the algebraic/homotopy theoretic formulation of the conjecture and the often very geometric proofs of instances of the conjecture. I plan to discuss this bridge in some detail.