TY - JOUR
T1 - Conjugacy, orbit equivalence and classification of measure-preserving group actions
AU - Törnquist, Asger Dag
PY - 2009/6/1
Y1 - 2009/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=69949086743&partnerID=8YFLogxK
U2 - 10.1017/S0143385708080528
DO - 10.1017/S0143385708080528
M3 - Journal article
AN - SCOPUS:69949086743
SN - 0143-3857
VL - 29
SP - 1033
EP - 1049
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 3
ER -