Related papers: Universal groups for right-angled buildings

In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local…

We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…

A universal group is a subgroup of the group of type preserving automorphisms of a right-angled building and hence associated to this building. A question is then if this universal group can act chamber-transitively and with compact open…

This article is an expanded version of the talks given by the authors at the Arbeitsgemeinschaft "Totally Disconnected Groups", held at Oberwolfach in October 2014. We recall the basic theory of automorphisms of trees and Tits' simplicity…

We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…

We introduce the notion of city products of right-angled buildings that produces a new right-angled building out of smaller ones. More precisely, if $M$ is a right-angled Coxeter diagram of rank $n$ and $\Delta_1,\dots,\Delta_n$ are…

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…

We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tree with nilpotent local action and no global fixed point is…

Bass-Serre theory provides a powerful framework for studying group actions on trees. While extremely effective for structural questions in group theory, it is less suited to the systematic construction of group actions with prescribed local…

We extend Burger--Mozes theory of closed, non-discrete, locally quasiprimitive automorphism groups of locally finite, connected graphs to the semiprimitive case, and develop a generalization of Burger--Mozes universal groups acting on the…

We introduce a class of spaces, called real cubings, and study the stucture of groups acting nicely on these spaces. Just as cubings are a natural generalisation of simplicial trees, real cubings can be regarded as a natural generalisation…

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…

Local actions (actions of a vertex stabiliser on the neighbours of that vertex) have become an important approach to group actions on trees since J. Tits' introduction in 1970 of the independence property (P) and especially since a 2000…

Burger and Mozes (1997) constructed the first examples of simple uniform lattices in products of trees. In this paper, we construct simple uniform lattices in products of certain Davis complexes. More precisely, we consider lattices in…

Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…

Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…

We construct a universal action of a countable locally finite group (the Hall's group) on a separable metric space by isometries. This single action contains all actions of all countable locally finite groups on all separable metric spaces…

We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

This article concerns Burger--Mozes universal groups acting on regular trees locally like a given permutation group of finite degree. We also consider locally isomorphic generalizations of the former due to Le Boudec and Lederle. For a…