K- and L-theory of group rings

Abstract

This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and Novikov Conjectures for topological rigidity. Its current status, and many of its consequences are surveyed.

25 pages, to appear in Proceedings of the ICM 2010

References in corpus (2)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Limit groups are CAT(0)