On the continuity of the growth rate on the space of Coxeter systems

IF 0.6 3区数学 Q3 MATHEMATICS Groups Geometry and Dynamics Pub Date : 2023-10-08 DOI:10.4171/ggd/741

Tomoshige Yukita

引用次数: 1

Abstract

Floyd showed that if a sequence of compact hyperbolic Coxeter polygons converges, then so does the sequence of the growth rates of the Coxeter groups associated with the polygons. For the case of the hyperbolic 3-space, Kolpakov discovered the same phenomena for specific convergent sequences of hyperbolic Coxeter polyhedra. In this paper, we show that the growth rate is a continuous function on the space of Coxeter systems. This is an extension of the results due to Floyd and Kolpakov since the convergent sequences of Coxeter polyhedra give rise to that of Coxeter systems in the space of marked groups.

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关于Coxeter系统空间上增长率的连续性

Floyd证明，如果紧致双曲Coxeter多边形序列收敛，那么与该多边形相关的Coxeter群的增长率序列也收敛。对于双曲三维空间，Kolpakov在特定的双曲Coxeter多面体收敛序列中发现了相同的现象。本文证明了增长率是Coxeter系统空间上的一个连续函数。这是Floyd和Kolpakov的结果的推广，因为Coxeter多面体的收敛序列会在标记群空间中产生Coxeter系统的收敛序列。

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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