# Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces

## TL;DR

This paper classifies all cobounded actions of solvable Baumslag-Solitar groups on hyperbolic spaces, revealing a finite set of action types and describing their partial order structure.

## Contribution

It provides a complete classification of these actions up to a natural equivalence, including the poset structure of the classes.

## Key findings

- Finitely many equivalence classes of actions.
- Actions are on a point, a tree, or the hyperbolic plane.
- Complete description of the poset of actions.

## 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.