Conjugacy, orbit equivalence and classification of measure-preserving group actions
Research output: Contribution to journal › Journal article › Research › peer-review
We prove that if G is a countable discrete group with property (T) over an infinite subgroup HG which contains an infinite Abelian subgroup or is normal, then G has continuum-many orbit-inequivalent measure-preserving almost-everywhere-free ergodic actions on a standard Borel probability space. Further, we obtain that the measure-preserving almost-everywhere-free ergodic actions of such a G cannot be classified up to orbit equivalence by a reasonable assignment of countable structures as complete invariants. We also obtain a strengthening and a new proof of a non-classification result of Foreman and Weiss for conjugacy of measure-preserving ergodic almost-everywhere-free actions of discrete countable groups.
Original language | English |
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Journal | Ergodic Theory and Dynamical Systems |
Volume | 29 |
Issue number | 3 |
Pages (from-to) | 1033-1049 |
Number of pages | 17 |
ISSN | 0143-3857 |
DOIs | |
Publication status | Published - 1 Jun 2009 |
ID: 61335006