Conjugacy, orbit equivalence and classification of measure-preserving group actions
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
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Tidsskrift | Ergodic Theory and Dynamical Systems |
Vol/bind | 29 |
Udgave nummer | 3 |
Sider (fra-til) | 1033-1049 |
Antal sider | 17 |
ISSN | 0143-3857 |
DOI | |
Status | Udgivet - 1 jun. 2009 |
ID: 61335006