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Orders on Trees and Free Products of Left-ordered Groups
Published online by Cambridge University Press: 31 March 2020
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.
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- © Canadian Mathematical Society 2019
Footnotes
The first-named author’s research was partially supported by Spain’s Ministerio de Ciencia e Innovación through Project MTM2011-25955. The second-named author’s research was partially supported by the National Science Foundation under Grant No. DMS-1105520
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