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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.
For an element in $BS(1,n) = langle t,a | tat^{-1} = a^n rangle$ written in the normal form $t^{-u}a^vt^w$ with $u,w geq 0$ and $v in mathbb{Z}$, we exhibit a geodesic word representing the element and give a formula for its word length with respect
We say that a group has property $R_{infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Felshtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{infty}$. We define a solvable
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notion of the best hyperbolic action of a group as the largest element of t
A generalized Baumslag-Solitar group is the fundamental group of a graph of groups all of whose vertex and edge groups are infinite cyclic. Levitt proves that any generalized Baumslag-Solitar group has property R-infinity, that is, any automorphism h
Recent papers of the authors have completely described the hyperbolic actions of several families of classically studied solvable groups. A key tool for these investigations is the machinery of confining subsets of Caprace, Cornulier, Monod, and Tess