论文标题
固体牙齿和轨道等效性刚度用于共同作用
Solid ergodicity and orbit equivalence rigidity for coinduced actions
论文作者
论文摘要
我们证明，对于相当大的共同诱导的作用，固体的牙齿性特性在诱导的共同诱导方面是稳定的。更确切地说，假设$σ<γ$是可计数的基团，以便$gσg^{ - 1} \capσ$对于任何$ g \inγ\setminusς$都是有限的。然后，当且仅当相关共同的共同行动的等价关系$γ\ curvearrowright x $时，任何保留动作的措施保存$σ\ curvearrowright x_0 $就会产生牢固的等价关系。我们还通过证明刚性或紧凑的度量保留动作的轨道等效关系$σ\ curvearrowrowrowrowrowrowrowrowrowrowrowrowrowrow x_0 $通过$ curvearrowrow x $ $γ\ curvearrowrow x $“记住”属性（t）组的轨道等效性关系$σ\ curvearrowrowrow x_0 $。
We prove that the solid ergodicity property is stable with respect to taking coinduction for a fairly large class of coinduced action. More precisely, assume that $Σ<Γ$ are countable groups such that $gΣg^{-1}\cap Σ$ is finite for any $g\inΓ\setminusΣ$. Then any measure preserving action $Σ\curvearrowright X_0$ gives rise to a solidly ergodic equivalence relation if and only if the equivalence relation of the associated coinduced action $Γ\curvearrowright X$ is solidly ergodic. We also obtain orbit equivalence rigidity for such actions by showing that the orbit equivalence relation of a rigid or compact measure preserving action $Σ\curvearrowright X_0$ of a property (T) group is "remembered" by the orbit equivalence relation of $Γ\curvearrowright X$.
