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Groups, Geometry, and Dynamics
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Published online: 2020-10-26
Hyperbolic immersions of free groups
Jean Pierre Mutanguha[1] (1) University of Arkansas, Fayetteville, USAWe 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