|Location:||UC Berkeley, 740 Evans Hall|
We give an introduction to the K- and L-theoretic Farrell-Jones Conjecture and discuss its status. e.g, recently it has been proved for all lattices in almost connected Lie groups. We give a panorama of its large variety of applications, for instance to the Novikov Conjecvture about the homotopy invariance of higher signatures, the Borel Conjecture about the
topological rigidity of aspherical manifolds and to hyperbolic groups with spheres as boundary. Finally we dicsuss some connections to equivariant homotopy and homology for proper actions of infinite groups.