Hyperbolic Immersions of Free Groups

Jean Pierre Mutanguha

Published 2018-09-13Version 1

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.