Abstract: The Farrell-Jones Conjecture predicts a homological formula for the K- and L-theory of group rings. It is connected to a number of other conjectures, for instance to Borel's Conjecture on the rigidity of aspherical manifolds, Novikov's Conjecture on the homotopy invarance of higher signatures and Kaplansky's conjecture on idempotents in group rings. In my talk I will give an introduction to the Farrell-Jones Conjecture. I will also discuss cases where this conjecture is know to hold and cases where the conjecture is still open.
