Coloured Neretin groups

Waltraud Lederle

doi:10.4171/GGD/495

Coloured Neretin groups

Waltraud Lederle

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We give sufficient conditions for a subgroup of a tree almost automorphism group to be isomorphic to the topological full groups of a one-sided shift in the sense of Matui. As an application, we show that almost automorphism groups of trees obtained from universal groups constructed by Burger and Mozes are compactly generated and virtually simple. In addition, using the approach of Bader, Caprace, Gelander and Mozes we show that some of these almost automorphism groups do not have any lattice.

Original language	English
Pages (from-to)	467-510
Number of pages	44
Journal	Groups, Geometry, and Dynamics
Volume	13
Issue number	2
DOIs	https://doi.org/10.4171/GGD/495
State	Published - 1 Jan 2019
Externally published	Yes

Keywords

Almost automorphisms
Groups acting on trees
Neretin’s group
Simple groups
Topological full groups

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/495

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AB - We give sufficient conditions for a subgroup of a tree almost automorphism group to be isomorphic to the topological full groups of a one-sided shift in the sense of Matui. As an application, we show that almost automorphism groups of trees obtained from universal groups constructed by Burger and Mozes are compactly generated and virtually simple. In addition, using the approach of Bader, Caprace, Gelander and Mozes we show that some of these almost automorphism groups do not have any lattice.

KW - Almost automorphisms

KW - Groups acting on trees

KW - Neretin’s group

KW - Simple groups

KW - Topological full groups

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Coloured Neretin groups

Abstract

Keywords

ASJC Scopus subject areas

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