Embedding finitely generated free-by-cyclic groups in finitely generated free-by-cyclic groups
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.
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