Hyperbolic Immersions of Free Groups

Abstract

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 $F_n$.

Argument streamlined and generalized; terminology changed; 19 pages, 4 figures

Cited by in corpus (1)

• The dynamics and geometry of free group endomorphisms