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Proceedings of the London Mathematical Society Advance Access published online on August 20, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp036
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© 2009 London Mathematical Society

Turbulence, representations, and trace-preserving actions

David Kerr

Department of Mathematics
Texas A&M University
College Station, TX 77843-3368
USA

Hanfeng Li

Department of Mathematics
SUNY at Buffalo
Buffalo, NY 14260-2900
USA
hfli@math.buffalo.edu

Mikaël Pichot

Department of Mathematical Sciences
University of Tokyo
3-8-1 Komaba
Tokyo 153-8914
Japan
pichot@ms.u-tokyo.ac.jp

Received 23 October 2008. Revision received 26 March 2009.

We establish criteria for turbulence in certain spaces of C*-algebra representations and apply this to the problem of nonclassifiability by countable structures for group actions on a standard atomless probability space (X, µ) and on the hyperfinite II1 factor R. We also prove that the conjugacy action on the space of free actions of a countably infinite amenable group on R is turbulent, and that the conjugacy action on the space of ergodic measure-preserving flows on (X, µ) is generically turbulent.

2000 Mathematics Subject Classification 22D10, 37A15, 46L55.


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