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arXiv · 1909.08716

Quotients by countable subgroups are hyperfinite

Joshua Frisch·Forte Shinko
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Abstract

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

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Joshua Frisch, Forte Shinko. 2020-02-21. Quotients by countable subgroups are hyperfinite. https://arxiv.org/abs/1909.08716

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