论文标题
在整个小组中密集的动力免费子组
On dense totipotent free subgroups in full groups
论文作者
论文摘要
我们研究了自由团体和相关IRS的概率度量保存（P.M.P.）。可数组伽玛的完美核是没有孤立点的伽玛亚组空间的最大封闭子空间。我们介绍了全能的Ergodic P.M.P.伽马的动作：几乎每个点稳定器都在完美内核中都有密集的共轭班的动作。同等地，关联的IRS的支持尽可能大，即它等于整个完美的内核。我们证明了每一个崇高的P.M.P.成本$ <r $的等价关系r可以通过自由组f_r在R发电机上的操作的轨道实现，并且整个组中的图像是密集的。我们解释了为什么这些动作没有最小的模型。这也提供了f_r的成对轨道不变的随机亚组的连续体，其所有支持都等于无限索引亚组的整个空间。我们被介绍了拓扑生成对完整组的属性（我们称之为逃生），并就其存在建立一般性结果。我们证明它们的存在特征成本1。
We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated points. We introduce the class of totipotent ergodic p.m.p. actions of Gamma: those for which almost every point-stabilizer has dense conjugacy class in the perfect kernel. Equivalently, the support of the associated IRS is as large as possible, namely it is equal to the whole perfect kernel. We prove that every ergodic p.m.p. equivalence relation R of cost $<r$ can be realized by the orbits of an action of the free group F_r on r generators that is totipotent and such that the image in the full group [R] is dense. We explain why these actions have no minimal models.This also provides a continuum of pairwise orbit inequivalent invariant random subgroups of F_r, all of whose supports are equal to the whole space of infinite index subgroups. We are led to introduce a property of topologically generating pairs for full groups (we call evanescence) and establish a genericity result about their existence. We show that their existence characterizes cost 1.
