逐元素保守动作与新的鼓浪子群构造
Elementwise conservative actions and new constructions of boomerang subgroups
AI总结：
本文研究了自由群中逐元素保守随机子群的构造，证明其在可测满群中的普遍性，并补充了高维晶格中相关刚性结果。
摘要：
我们证明可数非交换自由群允许不可数多个互不相容的逐元素保守非奇异随机子群，这些子群支持在无限子群上，且对每个不变随机子群都是奇异的。这补充了由第一和第三作者在高维晶格中关于逐元素保守随机子群的最近刚性结果。我们的证明基于对自由群到可测满群的表示研究，其中第一个生成元的动作被固定。我们证明在Baire范畴意义上，逐元素保守性在这些表示中是普遍的。
英文摘要：
We show that countable non-abelian free groups admit uncountably many mutually singular elementwise conservative non-singular random subgroups, which are supported on infinite subgroups of infinite index and singular with respect to every invariant random subgroup. This complements recent rigidity results for elementwise-conservative random subgroups in higher rank lattices by the first- and third-named authors. Our proof is based on a study of representations of free groups into measurable full groups in which the action of the first generator of the free group is fixed. We show that elementwise conservativity is generic among such representations in the sense of Baire category.
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