图乘积的层次双曲性

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-06-04 DOI:10.4171/ggd/652

D. Berlyne, Jacob Russell

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引用次数: 8

摘要

我们证明了有限生成群的任何图乘积相对于其顶点群都是层次双曲的。我们将这个结果应用于回答Behrstock、Hagen和Sisto的两个问题：我们证明了任何图乘积上的音节度量形成了一个层次双曲空间，并且层次双曲群的图乘积本身就是层次双曲群。最后一个结果是通过消除对顶点群的额外假设的需要来加强Berlai和Robio的结果。我们还回答了Genevois关于有限群的图乘积的带电几何的两个问题。

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Hierarchical hyperbolicity of graph products

We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this result to answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on any graph product forms a hierarchically hyperbolic space, and that graph products of hierarchically hyperbolic groups are themselves hierarchically hyperbolic groups. This last result is a strengthening of a result of Berlai and Robbio by removing the need for extra hypotheses on the vertex groups. We also answer two questions of Genevois about the geometry of the electrification of a graph product of finite groups.

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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.