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.
"Invariants of orbit equivalence relations and Baumslag-Solitar groups." Tohoku Math. J. (2) 66 (2) 205 - 258, 2014. https://doi.org/10.2748/tmj/1404911861