Higher rank confining subsets and hyperbolic actions of solvable groups

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 Tessera, which applies, in particular, to solvable gro...

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Published in:Advances in mathematics (New York. 1965) 2023-07, Vol.424, p.109045, Article 109045
Main Authors: Abbott, Carolyn R., H Balasubramanya, Sahana, Rasmussen, Alexander J.
Format: Article
Language:English
Subjects:
Baumslag-Solitar groups
Bieri-Neumann-Strebel invariants
Gromov hyperbolicity
Solvable groups
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Summary: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 Tessera, which applies, in particular, to solvable groups with virtually cyclic abelianizations. In this paper, we extend this machinery and give a correspondence between the hyperbolic actions of certain solvable groups with higher rank abelianizations and confining subsets of these more general groups. We then apply this extension to give a complete description of the hyperbolic actions of generalized solvable Baumslag-Solitar groups and to reprove a result of Sgobbi-Wong computing their Bieri-Neumann-Strebel invariants.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109045