Euclidean Artin–Tits groups are acylindrically hyperbolic

IF 0.6 3区数学 Q3 MATHEMATICS Groups Geometry and Dynamics Pub Date : 2020-10-25 DOI:10.4171/ggd/683

M. Calvez

引用次数: 7

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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欧几里得阿汀-山雀群呈非圆柱形双曲

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.

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