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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
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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