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Groups, Geometry, and Dynamics


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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