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 |
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Pages (from-to) | 467-510 |
Number of pages | 44 |
Journal | Groups, Geometry, and Dynamics |
Volume | 13 |
Issue number | 2 |
DOIs | |
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