Operator algebra seminar

Speaker: Markus Land (University of Regensburg)

Title: K- and L-theory for C*-algebras and assembly maps

Abstract: My goal for this talk is to describe a comparison between the Baum-Connes conjecture in topological K-theory and the Farrell-Jones conjecture in algebraic L-theory, which I proved in joint work with Thomas Nikolaus. The comparison relies on a relation between the topological K-theory and the algebraic L-theory for C*-algebras. Thus I will first try to give some background in algebraic L-theory and how it behaves for C*-algebras. Then I will explain how to use a homotopy theoretic version of the KK-category to prove that after inverting 2, topological K-theory and algebraic L-theory are equivalent. To apply this to the Baum-Connes and Farrell-Jones conjectures we need to provide a version of this equivalence starting from groupoids, which can be done by some concrete construction due to M. Joachim, but which actually follows from a homotopy theoretic theorem that I proved in joint work with Thomas Nikolaus and Karol Szumiło.