English

Train track maps on graphs of groups

Group Theory 2022-11-15 v3 Geometric Topology

Abstract

In this paper we develop the theory of train track maps on graphs of groups. Expanding 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.

Keywords

Cite

@article{arxiv.2102.02848,
  title  = {Train track maps on graphs of groups},
  author = {Rylee Alanza Lyman},
  journal= {arXiv preprint arXiv:2102.02848},
  year   = {2022}
}

Comments

26 pages, 3 figures. v3: revised according to referee comments v2: This paper has been split in two, with the second half, titled "CTs for free products," to appear on this arXiv

R2 v1 2026-06-23T22:51:09.181Z