Orbit inequivalent actions of non-amenable groups

Abstract

Consider two free measure preserving group actions $Γ\actson (X, μ), Δ\actson (X, μ)$, and a measure preserving action $Δ\actson^a (Z, ν)$ where $(X,\mu ),(Z,\nu )$ are standard probability spaces. We show how to construct free measure preserving actions $Γ\actson^c (Y, m)$, $Δ\actson^d (Y, m)$ on a standard probability space such that $E_{\Delta }^d\subset E_{\Gamma }^c$ and $d$ has $a$ as a factor. This generalizes the standard notion of co-induction of actions of groups from actions of subgroups. We then use this construction to show that if $\Gamma$ is a countable non-amenable group, then $\Gamma$ admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard probability space.

Wrote introduction, references, etc

References in corpus (1)

• Orbit inequivalent actions for groups containing a copy of ${\mathbb{F}}_2$

Cited by in corpus (1)

• Almost continuous orbit equivalence for non-singular homeomorphisms