论文标题
左端空间上的Borel结构
Borel structures on the space of left-orderings
论文作者
论文摘要
在本文中，我们研究了一组$ g $ modulo的左订购$ \ mathrm {lo}（g）$的Borel borel结构，自然结合行动，通过使用描述性集合理论的工具，我们发现了许多可数左订购组的示例，例如，商$ \ mathrm {lo mathrm {lo}（g）（g）/g是标准的。这回答了德罗因，纳瓦斯和里瓦斯的问题。我们还证明，$ \ mathbb {f} _ {2} $在$ \ mathrm {lo {lo}上（\ mathbb {f} _ {2}）$上的可数鲍勒等同性关系引起$ \ mathrm {lo}（g）$诱导通用可计数的bore等价关系。
In this paper we study the Borel structure of the space of left-orderings $\mathrm{LO}(G)$ of a group $G$ modulo the natural conjugacy action, and by using tools from descriptive set theory we find many examples of countable left-orderable groups such that the quotient space $\mathrm{LO}(G)/G$ is not standard. This answers a question of Deroin, Navas, and Rivas. We also prove that the countable Borel equivalence relation induced from the conjugacy action of $\mathbb{F}_{2}$ on $\mathrm{LO}(\mathbb{F}_{2})$ is universal, and leverage this result to provide many other examples of countable left-orderable groups $G$ such that the natural $G$-action on $\mathrm{LO}(G)$ induces a universal countable Borel equivalence relation.
