JournalsggdVol. 13, No. 4pp. 1219–1234

Non-classification of free Araki–Woods factors and -invariants

  • Román Sasyk

    CONICET and Universidad de Buenos Aires, Argentina

  • Asger Törnquist

    University of Copenhagen, Denmark

  • Stefaan Vaes

    Katholieke Universiteit Leuven, Belgium
Non-classification of free Araki–Woods factors and $\tau$-invariants cover
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Abstract

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 -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.

Cite this article

Román Sasyk, Asger Törnquist, Stefaan Vaes, Non-classification of free Araki–Woods factors and -invariants. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1219–1234

DOI 10.4171/GGD/520