## Non-classification of free Araki-Woods factors and τ-invariants

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We define the standard Borel space of free Araki-Woods factors and prove that their isomorphism relation is not classifiable by countable structures. We also prove that equality of τ-topologies, arising as invariants of type III factors, as well as cocycle and outer conjugacy of actions of abelian groups on free product factors are not classifiable by countable structures.

Originalsprog Engelsk Groups, Geometry, and Dynamics 13 4 1219-1234 1661-7207 https://doi.org/10.4171/GGD/520 Udgivet - 2019

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