CRC 878 B05 - K-theory, L-theory and assembly maps

Basic data for this project

Description

In this project we study algebraic K-theory, L-theory and applications thereof to manifolds and automorphisms of manifolds. To understand non-simply connected manifolds we study the K-and L-theory of group rings via the Farrell-Jones assembly map. We extend the context of the Farrell-Jones Conjecture, for example to Hecke algebras of reductive p-adic groups. We analyze the smooth structure space of manifolds in terms of L-theory and algebraic K-theory extending results of Weiss-Williams for topological manifolds.