Comptes Rendus
no. 12
Group theory/Geometry
Horofunctions on graphs of linear growth

Presented by: the Editorial Board

Matthew C.H. Tointon1; Ariel Yadin2
1 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
2 Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1151-1154.

We prove that a linear growth graph has finitely many horofunctions. This provides a short and simple proof that any finitely generated infinite group of linear growth is virtually cyclic.

Nous montrons qu'un graphe à croissance linéaire admet un nombre fini d'horofonctions. Cela donne une preuve courte et simple que chaque groupe infini de type fini à croissance linéaire est virtuellement cyclique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.015

Matthew C.H. Tointon 1; Ariel Yadin 2

1 Laboratoire de mathématiques d'Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
2 Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel 
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Matthew C.H. Tointon; Ariel Yadin. Horofunctions on graphs of linear growth. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1151-1154. doi : 10.1016/j.crma.2016.10.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.015/

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