Orders on trees and free products of left-ordered groups
Group Theory
2020-04-29 v2
Abstract
We construct total orders on the vertex set of an oriented tree. The orders are based only on up-down counts at the interior vertices and the edges along the unique geodesic from a given vertex to another. As an application, we provide a short proof (modulo Bass-Serre theory) of Vinogradov's result that the free product of left-orderable groups is left-orderable.
Keywords
Cite
@article{arxiv.1405.1676,
title = {Orders on trees and free products of left-ordered groups},
author = {Warren Dicks and Zoran Sunic},
journal= {arXiv preprint arXiv:1405.1676},
year = {2020}
}