在组图上绘制火车轨道图

Pub Date : 2021-02-04 DOI:10.4171/ggd/698

Rylee Alanza Lyman

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引用次数: 5

摘要

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。

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Train track maps on graphs of groups

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.

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