Date of Graduation
Doctor of Philosophy in Mathematics (PhD)
Second Committee Member
ascending HNN extensions, endomorphisms, free groups, geometric group theory, Gromov's question, mapping torus
We prove that ascending HNN extensions of free groups are word-hyperbolic if and only if they have no Baumslag-Solitar subgroups. This extends Brinkmann's theorem that free-by-cyclic groups are word-hyperbolic if and only if they have no Z2 subgroups. To get started on our main theorem, we first prove a structure theorem for injective but nonsurjective endomorphisms of free groups. With the decomposition of the free group given by this structure theorem, we (more or less) construct representatives for nonsurjective endomorphisms that are expanding immersions relative to a homotopy equivalence. This structure theorem initializes the development of (relative) train track theory for nonsurjective endomorphisms.
Mutanguha, J. (2020). Hyperbolic Endomorphisms of Free Groups. Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/3641