Groups acting on trees with almost prescribed local action
Group Theory
2016-02-18 v2
Abstract
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.
Cite
@article{arxiv.1505.01363,
title = {Groups acting on trees with almost prescribed local action},
author = {Adrien Le Boudec},
journal= {arXiv preprint arXiv:1505.01363},
year = {2016}
}
Comments
v2: 35 pages; argument slightly modified in 4.2.2; final version