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arXiv · 2306.12192

Groups Acting Acylindrically on Trees

William D. Cohen
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Abstract

We develop a notion of groups that act acylindrically and non-elementarily on simplicial trees, which we call acylindrically arboreal groups. We then prove a complete classification of when graph products of groups and the fundamental groups of certain hyperbolic $3$-manifolds are acylindrically arboreal, and use these classifications to provide examples of acylindrically hyperbolic groups that have actions on trees but have no non-elementary acylindrical actions on trees.

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William D. Cohen. 2023-06-21. Groups Acting Acylindrically on Trees. https://doi.org/10.1515/jgth-2024-0133

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