Conjugacy, orbit equivalence and classification of measure-preserving group actions

被引:4
|
作者
Toernquist, Asger [1 ]
机构
[1] Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada
关键词
PROPERTY;
D O I
10.1017/S0143385708080528
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove that if G is a Countable discrete group with property (T) over all infinite subgroup H <= G 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-every where-free actions of discrete countable groups.
引用
收藏
页码:1033 / 1049
页数:17
相关论文
共 50 条