We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag–Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of and nonsurjective fully irreducible endomorphisms of . We also give a framework for extending the theorem to all injective endomorphisms of .
Cite this article
Jean Pierre Mutanguha, Hyperbolic immersions of free groups. Groups Geom. Dyn. 14 (2020), no. 4, pp. 1253–1275DOI 10.4171/GGD/580