On the Farrell-Jones Conjecture and its applications, by Arthur Bartels, Wolfgang Lück, and Holger Reich

We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new applications, focusing on the Bass Conjecture, the Kaplansky Conjecture and conjectures generalizing Moody's Induction Theorem. Thus we extend the class of groups for which these conjectures are known considerably.

Arthur Bartels <bartelsa@math.uni-muenster.de>
Wolfgang Lück <lueck@math.uni-muenster.de>
Holger Reich <holger.reich@googlemail.com>