Compact presentability of tree almost automorphism groups
Abstract
We establish compact presentability, i.e. the locally compact version of finite presentability, for an infinite family of tree almost automorphism groups. Examples covered by our results include Neretin's group of spheromorphisms, as well as the topologically simple group containing the profinite completion of the Grigorchuk group constructed by Barnea, Ershov and Weigel. We additionally obtain an upper bound on the Dehn function of these groups in terms of the Dehn function of an embedded Higman-Thompson group. This, combined with a result of Guba, implies that the Dehn function of the Neretin group of the regular trivalent tree is polynomially bounded.
Cite
@article{arxiv.1402.5652,
title = {Compact presentability of tree almost automorphism groups},
author = {Adrien Le Boudec},
journal= {arXiv preprint arXiv:1402.5652},
year = {2016}
}
Comments
The results are extended to some almost automorphism groups of trees associated with closed regular branch groups. In particular we prove that the simple group (containing the profinite completion of the Grigorchuk group) constructed by Barnea, Ershov and Weigel, is compactly presented