论文标题
Cantor行动的基本人数
Essential holonomy of Cantor actions
论文作者
论文摘要
如果具有非平凡全体性的点集有积极的措施，则小组行动具有必不可少的载体。如果这样的动作在拓扑上是没有的，那么具有必不可少的人数等同于不是基本上自由的，这意味着具有非平凡稳定剂的点集具有积极的措施。在本文中，我们研究了具有最小值的综合作用在cantor套装上具有最小的等准作用的代理组的特性与结构之间的关系。我们表明，如果这样的小组作用是局部准分析并且具有必不可少的全体作用，那么小组较低中心系列中的每个换向子亚组都具有具有非平凡全体性的积极度量的元素。特别是，这给出了一个新的证据，表明，尼尔植物群体最少的等效康托尔动作没有基本的自由学。我们还表明，具有必要的全能性的特性是在返回等效性和最小等效cantor作用的连续轨道等效性下保留的。最后，我们举例说明，关于其局部准分析的作用的假设是必要的。
A group action has essential holonomy if the set of points with non-trivial holonomy has positive measure. If such an action is topologically free, then having essential holonomy is equivalent to the action not being essentially free, which means that the set of points with non-trivial stabilizer has positive measure. In this paper, we investigate the relation between the property of having essential holonomy and structure of the acting group for minimal equicontinuous actions on Cantor sets. We show that if such a group action is locally quasi-analytic and has essential holonomy, then every commutator subgroup in the group lower central series has elements with positive measure set of points with non-trivial holonomy. In particular, this gives a new proof that a minimal equicontinuous Cantor action by a nilpotent group has no essential holonomy. We also show that the property of having essential holonomy is preserved under return equivalence and continuous orbit equivalence of minimal equicontinuous Cantor actions. Finally, we give examples to show that the assumption on the action that it is locally quasi-analytic is necessary.
