Geodesic
Orders on Trees and Free Products of Left-ordered Groups
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 335-347

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/S0008439519000389
Mots-clés : orderable groups, free products, actions on trees, Bass–Serre tree 
Dicks, Warren; Šunić, Zoran. Orders on Trees and Free Products of Left-ordered Groups. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 335-347. doi: 10.4153/S0008439519000389
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