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arXiv · 2607.04300

Topological full groups and stable rank one

David Kerr·Spyridon Petrakos
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Abstract

We establish stable rank one for the reduced group C$^*$-algebras of the C$^*$-simple topological full groups and dynamical alternating groups constructed by Kerr and Tucker-Drob. The proof relies on both type II$_1$ and type III phenomena, in the first case via the use of F{\o}lner towers and in the second via Ozawa's recent results on selflessness as applied to direct products of free products.

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David Kerr, Spyridon Petrakos. 2026-07-05. Topological full groups and stable rank one. https://arxiv.org/abs/2607.04300

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