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The geometry of subgroups of free-by-cyclic groups

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OGG - Operators, Graphs, Groups

The well-known subgroup tameness theorem for hyperbolic 3-manifold groups characterises precisely when a finitely generated subgroup is quasi-convex. As a corollary, one can obtain a characterisation of hyperbolic 3-manifold groups that are locally quasi-convex as those that do not contain {compact surface}-by-cyclic subgroups. Although a version of the subgroup tameness theorem for the class of free-by-cyclic groups remains a difficult open problem, I will instead show that an analogous characterisation of local quasi-convexity amongst free-by-cyclic groups does indeed hold. I will explain the ideas that go into the proof, discuss a generalisation to the relatively hyperbolic setting and mention some applications to one-relator groups.

This talk is part of the Isaac Newton Institute Seminar Series series.

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