Groups acting on trees with almost prescribed local action

By Adrien Le Boudec. 2015

51 citations recorded by the source corpus.

We investigate a family of groups acting on a regular tree, defined by prescribing the local action almost everywhere. We study lattices in these groups and give examples of compactly generated simple groups of finite asymptotic dimension (actually one) not containing lattices. We also obtain examples of simple groups with simple lattices, and we prove the existence of (infinitely many) finitely generated simple groups of asymptotic dimension one. We also prove various properties of these groups, including the existence of a proper action on a CAT(0) cube complex.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6f274c5bda4c6b903db9e10cad523e164359a657

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-simplicity and the amenable radical (2016, unknown): “It is not hard to check that the fixator of e in G(F, F ′) is the product of the fixators of the two half-trees defined by e (in other words, the group G(F, F ′) has the edge-independence property in the terminology of [16]).”
Hyperbolic structures on groups (2017, background): “For instance, for any simply transitive subgroup F ≤ Sn, the group G = G(F ) ≤ Aut(T ) considered in [12] is finitely generated by [12, Corollary 3.”
On the joint spectral radius for isometries of non-positively curved spaces and uniform growth (2018, unknown): “These groups, denoted by G(F, F ′), in [60] have attracted a lot of attention lately.”