Orders on trees and free products of left-ordered groups

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.

Cited by in corpus (2)

• Intersections of subgroups in virtually free groups and virtually free products
• An analogue of the strengthened Hanna Neumann conjecture for virtually free groups and virtually free products