Title：Topological K-theory of discrete groups
Reporter：Bailing Wang
Work Unit：The Australian National University
Time：2023/05/19 10:30-11:30
Address：Tencent Meeting Id：516-539-518
Summary of the report:
In the 1980’s motivate by the Atiyah-Singer index formula, Baum and Connes constructed a topological K-theory of a discrete group $\Gamma$, together with an assembly map $\mu$ from this mysterious group to the K-theory group of the reduced C^∗ -algebra of $\Gamma$. They conjectured that this assembly map is an isomorphism. The validity of this conjecture implies Novikov conjecture, Gromov-Lawson-Rosenberg conjecture and Kadison-Kaplansky conjecture.
The mathematical details of this construction and the well-definedness of the assembly map were somewhat missing in their original paper. I will briefly explain some of my earlier work with Paulo Carrillo Rouse on filling up these details, and some recent work with Paulo Carrillo Rouse and Hang Wang on an assembly map to periodic cyclic homology and the Chern-Connes pairing formula for any discrete group.
Introduction of the Reporter: Bailing Wang is a professor at Australian National University. In April 1998, he graduated from the University of Adelaide, Australia with a PhD. After graduation, he worked as a postdoctoral fellow and visiting scholar at Max Planck Institute in Bonn, Germany, Institut des Sciences Superieure de France and University of Zurich. He has worked at the Australian National University since 2005. He mainly studies the topological invariants of gauge field theory in low dimensional topology, twisted K-homology and twisted index theory, Gromov-Witten modular space and the K-theory of Hamilton Gromov-Witten modular space.
