Actions of solvable Baumslag–Solitar groups on hyperbolic metric spaces

Abbott, Carolyn R; Rasmussen, Alexander J

doi:10.2140/agt.2023.23.1641

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Actions of solvable Baumslag–Solitar groups on hyperbolic metric spaces

Carolyn R Abbott and Alexander J Rasmussen

Algebraic & Geometric Topology 23 (2023) 1641–1692

DOI: 10.2140/agt.2023.23.1641

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 and 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

Baumslag–Solitar groups, hyperbolic metric spaces, Bass–Serre theory, solvable groups, p-adic numbers

Mathematical Subject Classification 2010

Primary: 20E06, 20E08, 20F16, 20F65

References

Publication

Received: 11 December 2019

Revised: 14 April 2021

Accepted: 5 October 2021

Published: 14 June 2023

Authors

Carolyn R Abbott
Department of Mathematics Brandeis University Waltham, MA United States

Alexander J Rasmussen
Department of Mathematics University of Utah Salt Lake City, UT United States

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Volume 23, issue 4 (2023)