Arthur Bartels: K-Theory of Group Rings
Explore the fourth lecture in a series on K-theory of group rings, delivered by Arthur Bartels as part of the Hausdorff Trimester Program: K-Theory and Related Fields. Delve into the Farrell-Jones Conjecture, which proposes that the K-theory of group rings RG can be calculated using the K-theory of group rings RV, where V represents various virtually cyclic subgroups of G. Examine the conjecture's formulation and proof methods, with a particular focus on controlled algebra. Understand how controlled algebra serves as a crucial link between the algebraic and homotopy theoretic formulation of the conjecture and the often geometric proofs of its instances. Gain insights into this complex mathematical topic through this 58-minute lecture from the Hausdorff Center for Mathematics.