About the Unit- and the Farrell-Jones Conjecture

In the "Quanta Magazine", Erica Klarreich and other mathematically educated science journalists introduce from time to time research results of pure mathematics, which are usually hard accessible for non-experts. Recently, there was a very interesting article about the disproof of the 80 years old Kaplansky 's unit conjecture through a computerized counterexample found by the postdoctoral researcher Giles Gardam from Münster:

Article on Quanta Magazine

The conjecture states that a group ring of a torsion-free group has no units except the trivial ones (the multiple of the group elements with the units of the rings). As the Farrell-Jones conjecture is closely related to the unit conjecture, Wolfgang Lück who has been researching this for years, was interviewed for this article and even quoted. The Farrell-Jones conjecture is sadly not as easily stated as the unit conjecture. It claims that the algebraic K- and L-theory of groups are isomorphic to certain calculable homology groups, leading to many applications to algebraic and topological problems. The Farrell-Jones conjecture also implies the famous Borel conjecture about aspherical manifolds. This is enough reason for us to investigate the concrete connection between the unit conjecture and the Farrell-Jones conjecture and how surprised Wolfgang Lück was about the counterexample to the former.

Please click here for the interview.