The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Groups, Geometry, and Dynamics

Full-Text PDF (322 KB) | Metadata | Table of Contents | GGD summary
Volume 14, Issue 4, 2020, pp. 1253–1275
DOI: 10.4171/GGD/580

Published online: 2020-10-26

Hyperbolic immersions of free groups

Jean Pierre Mutanguha[1]

(1) University of Arkansas, Fayetteville, USA

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 $F_2$ and nonsurjective fully irreducible endomorphisms of $F_n$. We also give a framework for extending the theorem to all injective endomorphisms of $F_n$.

Keywords: Nonsurjective endomorphisms, graph immersions, combination theorem, word-hyperbolic

Mutanguha Jean Pierre: Hyperbolic immersions of free groups. Groups Geom. Dyn. 14 (2020), 1253-1275. doi: 10.4171/GGD/580