Train track maps on graphs of groups

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2021-02-04 DOI:10.4171/ggd/698

Rylee Alanza Lyman

引用次数: 5

Abstract

In this paper we develop the theory of train track maps on graphs of groups. Ex-panding a deﬁnition of Bass, we deﬁne a notion of a map of a graph of groups, and of a homotopy equivalence. We prove that under one of two technical hypotheses, any homotopy equivalence of a graph of groups may be represented by a relative train track map. The ﬁrst applies in particular to graphs of groups with ﬁnite edge groups, while the second applies in particular to certain generalized Baumslag–Solitar groups.

查看原文本刊更多论文

在组图上绘制火车轨道图

本文在群图上发展了列车轨道图的理论。在推广Bass的定义时，我们定义了群图的映射和同伦等价的概念。我们证明了在两个技术假设中的一个条件下，群图的任何同伦等价都可以用相对的列车轨道图来表示。第一种方法特别适用于具有有限边群的群的图，而第二种方法特别应用于某些广义Baumslag–Solitar群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.