Non-inner amenability of the Higman-Thompson groups

Eli Bashwinger; Matthew C. B. Zaremsky

paper

Non-inner amenability of the Higman-Thompson groups

arXiv:2203.13798

Abstract

We prove that the Higman-Thompson groups $T_{n}$ and $V_{n}$ are non-inner amenable for all $n \geq 2$ . This extends Haagerup and Olesen's result that Thompson's groups $T = T_{2}$ and $V = V_{2}$ are non-inner amenable. Their proof relied on machinery only available in the $n = 2$ case, namely Thurston's piecewise-projective model for Thompson's group $T$ , so our approach necessarily utilizes different tools. This also provides an alternate proof of Haagerup-Olesen's result when $n = 2$ .

10 pages, 2 figures. v2: minor changes, accepted version, to appear in IJAC