Non-inner amenability of the Higman-Thompson groups

2022/03/25 by Eli Bashwinger, Matthew C. B. Zaremsky, Bashwinger, Eli +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Advanced Materials and Mechanics #Connective tissue disorders research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2203.13798

openalex publication_date 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Higman-Thompson groups T_n and V_n are non-inner amenable for all n≥ 2. This extends Haagerup and Olesen's result that Thompson's groups T=T₂ and V=V₂ 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.

Cited by

• Non-strong ergodicity of canonical actions of the Thompson groups
• On Similarity Structure Groups and their W^* and C^*-Algebras

Related

• Non-inner amenability of the Thompson groups T and V
• The Inner Amenability of the Generalized Thompson Group
• Non-amenability of R.Thompson's group F
• Richard Thompson group F is not amenable
• New embeddings between the Higman-Thompson groups