On the Farrell-Jones Conjecture for higher algebraic K-Theory

The Farrell-Jones Conjecture predicts that the algebraic K-Theory of a group ring RG can be expressed in terms of the algebraic K-Theory of the coefficient ring R and homological information about the group. After an introduction to this circle of ideas the talk will report on recent joint work with A. Bartels which builds up on earlier joint work with A. Bartels, T. Farrell and L. Jones. We prove that the Farrell-Jones Conjecture holds in the case where the group is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The result holds for all of K-Theory, in particular for higher K-Theory, and for arbitrary coefficient rings R.