Quotients by countable subgroups are hyperfinite

Abstract

We show that for any Polish group $G$ and any countable normal subgroup $\Gamma ◃G$, the coset equivalence relation $G/\Gamma$ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any countable group is hyperfinite.

7 pages; corrected implication (discrete -> smooth)