Compact presentability of tree almost automorphism groups

2014/02/23 by Adrien Le Boudec, Boudec, Adrien Le · 2 citations
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1402.5652

openalex publication_date 2014/02/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We establish compact presentability, i.e. the locally compact version of finite presentability, for an infinite family of tree almost automorphism groups. Examples covered by our results include Neretin's group of spheromorphisms, as well as the topologically simple group containing the profinite completion of the Grigorchuk group constructed by Barnea, Ershov and Weigel. We additionally obtain an upper bound on the Dehn function of these groups in terms of the Dehn function of an embedded Higman-Thompson group. This, combined with a result of Guba, implies that the Dehn function of the Neretin group of the regular trivalent tree is polynomially bounded.

Cited by

• Infinitely presented simple groups separated by homological finiteness properties
• The regular representation of Neretin groups is factorial

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• Coloured Neretin Groups
• Topological models of finite type for tree almost automorphism groups
• Automorphism Groups of Trees: Generalities and Prescribed Local Actions
• Commensurated subgroups in tree almost automorphism groups
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