K-theory, L-theory and assembly maps (B05)

• Subject Area: Mathematics
• Term: from 2010 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 129719356

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.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 878: Groups, Geometry and Actions
• Applicant Institution: Universität Münster
• Project Heads: Professor Dr. Arthur Bartels, since 10/2017; Professor Dr. Wolfgang Lück, until 9/2010; Professor Dr. Michael Weiss