Actions of solvable groups on hyperbolic spaces

Abstract: Recent papers of Balasubramanya and Abbott-Rasmussen have classified 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-Tessera. This machinery applies in particular to solvable groups with virtually cyclic abelianizations.

In this talk, my goal is to explain how to extend this machinery to classify the hyperbolic actions of certain solvable groups with higher rank abelianizations. We apply this extension to classify the hyperbolic actions of a family of groups related to Baumslag-Solitar groups.

The first half of the talk will cover the required preliminary information and some of the known results concerning the hyperbolic actions of certain solvable groups. In the second half, I shall explain the techniques used to prove the aforementioned results. Lastly, I shall talk about the new results that we prove in our paper that generalize these techniques.

(joint work with A.Rasmussen and C.Abbott)

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar