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Hyperbolic Immersions of Free Groups

Abstract: We prove that the mapping torus of a graph immersion has word-hyperbolic fundamental group if and only if the corresponding endomorphism doesn't produce Baumslag-Solitar subgroups. Due to a result by Reynolds, this theorem applies to all nonsurjective fully irreducible endomorphisms. We also give a framework for proving the general statement without the immersion assumption.

Last updated: Fri 14 June 2019