Veranstaltungen am Mathematischen Institut

Abstract: The Higman-Thompson groups consist of certain piecewise linear automorphisms of intervals. Szymik and Wahl prove homological stability for this family of groups, and compute the stable homology to be that of the infinite loop space of the Moore spectrum. We give a new proof of this result using scanning methods on a topological model for the disjoint union of these groups, using Thumann's framework of operad groups.

I'll give an overview of stable rank one and the C*-algebras known to have it, then describe a new approach to studying stable rank one in possibly nonnuclear crossed products. As an application, we show that stable rank one is generic for two natural classes of minimal actions of free groups on the Cantor set. Time permitting, I will discuss some examples to motivate parts of the proof. This is joint work with Shirly Geffen and David Kerr.