Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity [article]

Cyril Houdayer, Sven Raum
2015 arXiv   pre-print
We introduce an algebraic invariant for aperiodic inclusions of probability measure preserving equivalence relations. We use this invariant to prove that every stable orbit equivalence between free pmp actions of direct products of non-amenable Baumslag-Solitar groups whose canonical subgroup acts aperiodically forces the number of factors of the products to be the same and the factors to be isomorphic after permutation. This generalises some of the results obtained by Kida and moreover
more » ... new measure equivalence rigidity phenomena for Baumslag-Solitar groups. We also obtain a complete classification of direct products of relative profinite completions of Baumslag-Solitar groups, continuing recent work of Elder and Willis.
arXiv:1308.5855v4 fatcat:3xax4we3sbhnfgdwqiiy2rw45e