Train track maps on graphs of groups

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.

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

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