3-Manifold Groups Acting Acylindrically on Trees

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• William Cohen, University of Cambridge
• Friday 06 October 2023, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

It was shown by Balasubramanya that any acylindrically hyperbolic group must act acylindrically and non-elementarily on some quasi-tree. It is therefore sensible to ask to what extent this is true for trees, i.e. given an acylindrically hyperbolic group, does it admit a non-elementary acylindrical action on some simplicial tree? In this talk I will introduce the concept of an acylindrically arboreal group and consider some examples of acylindrically hyperbolic groups which do and do not act acylindrically on trees. I will then present a characterisation of when exactly the fundamental groups of closed and orientable hyperbolic 3-manifolds act acylindrically and non-elementarily on trees based entirely on the geometry of the 3-manifolds in question.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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