Stable homology of Higman--Thompson groups via scanning methods

Abstract

The Higman--Thompson groups $V_{n,r}$ consist of piecewise linear automorphisms of $r$ intervals where cut points and slopes are $n$-adic. Szymik and Wahl prove homological stability for this family of groups as $r$ increases, 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. We use Thumann's framework of operad groups to build this model.