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 F2 and nonsurjective fully irreducible endomorphisms of Fn.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Combination theorem
- Graph immersions
- Nonsurjective endomorphisms