Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces
Group Theory
2023-06-21 v2 Geometric Topology
Metric Geometry
Abstract
We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classes carries a natural partial order first introduced by Abbott-Balasubramanya-Osin, and we describe the resulting poset completely. There are finitely many equivalence classes of actions, and each equivalence class contains the action on a point, a tree, or the hyperbolic plane.
Keywords
Cite
@article{arxiv.1906.04227,
title = {Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces},
author = {Carolyn R. Abbott and Alexander J. Rasmussen},
journal= {arXiv preprint arXiv:1906.04227},
year = {2023}
}
Comments
Final version, to appear in Algebraic & Geometric Topology