Higher rank confining subsets and hyperbolic actions of solvable groups

Recent papers of the authors have completely described hyperbolic actions several families classically studied solvable groups. A key tool for these investigations is machinery confining subsets Caprace, Cornulier, Monod, and Tessera, which applies, in particular, to groups with virtually cyclic abelianizations. In this paper, we extend give a correspondence between certain higher rank abelianizations more general We then apply extension complete description generalized Baumslag-Solitar reprove result Sgobbi-Wong computing their Bieri-Neumann-Strebel invariants.