Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups
Group Theory
2026-04-23 v2
Abstract
We refine Feighn--Handel's results on subgroups of mapping tori of free groups to the special case of free-by-cyclic groups. We use these refinements to show that any finitely generated free-by-cyclic group embeds in a {finitely generated free}-by-cyclic group. When the free-by-cyclic group is hyperbolic, it embeds in a hyperbolic {finitely generated free}-by-cyclic group as a quasi-convex subgroup. Combined with a result of Hagen--Wise, this implies that all hyperbolic free-by-cyclic groups are cocompactly cubulated.
Cite
@article{arxiv.2510.10178,
title = {Embedding finitely generated free-by-cyclic groups in {finitely generated free}-by-cyclic groups},
author = {Marco Linton},
journal= {arXiv preprint arXiv:2510.10178},
year = {2026}
}
Comments
17 pages. Slightly improved main theorem. Version accepted for publication at Int. Math. Res. Not