Mathematics > Operator Algebras
[Submitted on 27 Feb 2007 (v1), last revised 18 Mar 2008 (this version, v3)]
Title:Conjugacy, orbit equivalence and classification of measure preserving group actions
View PDFAbstract: We prove that if $G$ is a countable discrete group with property (T) over an infinite subgroup $H<G$ which contains an infinite Abelian subgroup or is normal, then $G$ has continuum many orbit inequivalent measure preserving a.e. free ergodic actions on a standard Borel probability space. Further, we obtain that the measure preserving a.e. free ergodic actions of such a $G$ cannot be classified up to orbit equivalence be 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, a.e. free actions of discrete countable groups.
Submission history
From: Asger Tornquist [view email][v1] Tue, 27 Feb 2007 23:38:21 UTC (25 KB)
[v2] Mon, 3 Dec 2007 03:15:32 UTC (25 KB)
[v3] Tue, 18 Mar 2008 01:49:57 UTC (15 KB)
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