Invariants of orbit equivalence relations and Baumslag-Solitar groups

Abstract

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of Baumslag-Solitar groups under weak orbit equivalence. Results on groups which are measure equivalent to Baumslag-Solitar groups are also provided.

49 pages, minor corrections

References in corpus (6)

• Non-ergodic actions, cocycles and superrigidity
• A spectral sequence to compute L2-Betti numbers of groups and groupoids
• Orbit equivalence rigidity for ergodic actions of the mapping class group
• Rigidity of amalgamated free products in measure equivalence
• Examples of amalgamated free products and coupling rigidity
• Integrable measure equivalence and rigidity of hyperbolic lattices

Cited by in corpus (5)

• Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups
• Inner amenable groups having no stable action
• Measure equivalence classification of transvection-free right-angled Artin groups
• Stable actions of central extensions and relative property (T)
• Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity