欧几里得阿汀-山雀群呈非圆柱形双曲

Pub Date : 2020-10-25 DOI:10.4171/ggd/683
M. Calvez
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引用次数: 7

摘要

在本文中,我们展示了标题中的语句。对于任何有限型Garside群,Wiest和作者关联了一个称为\emph{附加长度图}的双曲图,并用它证明了球面型Artin-Tits群的中心商是非圆柱形双曲的。一般来说,欧几里得Artin-Tits\emph{群不是先天}的Garside群,但McCammond和Sulway已经证明,它嵌入到\emph{无限型}Garside群中,他们称之为\emph{晶体Garside群}。我们将一个\emph{双曲}附加长度图与这个晶体Garside群联系起来,并展示了欧几里得Artin-Tits群的元素,这些元素在双曲图上表现为线性和WPD。
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Euclidean Artin–Tits groups are acylindrically hyperbolic
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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