Groups Acting Acylindrically on Trees
Group Theory
2026-01-16 v6 Geometric Topology
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 -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.
Cite
@article{arxiv.2306.12192,
title = {Groups Acting Acylindrically on Trees},
author = {William D. Cohen},
journal= {arXiv preprint arXiv:2306.12192},
year = {2026}
}
Comments
Version to appear in Journal of Group Theory. 27 Pages, 2 figures