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arXiv · 2010.13145

Euclidean Artin-Tits groups are acylindrically hyperbolic

Matthieu Calvez
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Abstract

In this paper we show the statement in the title. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called the \emph{additional length graph} and they used it to show that central quotients of Artin-Tits groups of spherical type are acylindrically hyperbolic. In general, a euclidean Artin-Tits group is not \emph{a priori} a Garside group but McCammond and Sulway have shown that it embeds into an \emph{infinite-type} Garside group which they call a \emph{crystallographic Garside group}. We associate a \emph{hyperbolic} additional length graph to this crystallographic Garside group and we exhibit elements of the euclidean Artin-Tits group which act loxodromically and WPD on this hyperbolic graph.

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Matthieu Calvez. 2020-10-25. Euclidean Artin-Tits groups are acylindrically hyperbolic. https://arxiv.org/abs/2010.13145

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