Stable homology of Higman--Thompson groups via scanning methods

Marie-Camille Delarue

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arXiv · 2510.13579

Stable homology of Higman--Thompson groups via scanning methods

Marie-Camille Delarue

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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.

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Marie-Camille Delarue. 2025-10-15. Stable homology of Higman--Thompson groups via scanning methods. https://arxiv.org/abs/2510.13579

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