Hyperbolic quotients of projection complexes

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-05-28 DOI:10.4171/ggd/646

Matt Clay, J. Mangahas

引用次数: 5

Abstract

This paper is a continuation of our previous work with Margalit where we studied group actions on projection complexes. In that paper, we demonstrated sufficient conditions so that the normal closure of a family of subgroups of vertex stabilizers is a free product of certain conjugates of these subgroups. In this paper, we study both the quotient of the projection complex by this normal subgroup and the action of the quotient group on the quotient of the projection complex. We show that under certain conditions that the quotient complex is $\delta$-hyperbolic. Additionally, under certain circumstances, we show that if the original action on the projection complex was a non-elementary WPD action, then so is the action of the quotient group on the quotient of the projection complex. This implies that the quotient group is acylindrically hyperbolic.

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投影复合体的双曲商

这篇论文是我们之前在Margalit研究投影复合体上的群作用的工作的延续。在这篇文章中，我们证明了顶点稳定器子群族的正规闭包是这些子群的某些共轭的自由乘积的充分条件。本文研究了此正规子群的投影复形的商，以及商群对投影复形商的作用。我们证明了在一定条件下商复形是$\delta$-双曲的。此外，在某些情况下，我们证明了如果投影复数上的原始作用是非初等WPD作用，那么商群对投影复数的商的作用也是如此。这意味着商群是非圆柱双曲的。

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.