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Friday, October 18, 2019
2:00 PM - 3:30 PM

# Caltech-UCLA Logic Seminar

Quotients by countable subgroups are hyperfinite
Shinko Forte, Department of Mathematics, Caltech,

UCLA, MS 6221

Given a countable group Gamma, the outer automorphism group Out(Gamma) is either countable or of cardinality continuum. A finer and more suitable notion is to consider the Borel complexity of Out(Gamma) as a Borel equivalence relation. We show that in this context, Out(Gamma) is of rather low complexity, namely that it is a hyperfinite Borel equivalence relation. In general, we show that for any Polish group G and any countable normal subgroup Gamma, the quotient group G/Gamma is hyperfinite. This is joint work with Joshua Frisch.