تقرير
Borel structures on the space of left-orderings
| العنوان: | Borel structures on the space of left-orderings |
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| المؤلفون: | Calderoni, Filippo, Clay, Adam |
| المصدر: | Bull. London Math. Soc., 54(1): 83-94, 2022 |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Logic, 03E15, 06F15, 20F60, 54H05 |
| الوصف: | 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. Comment: Example 2.10 was fixed. This version supersedes the published version |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1112/blms.12559 |
| URL الوصول: | http://arxiv.org/abs/2002.02565 |
| رقم الأكسشن: | edsarx.2002.02565 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1112/blms.12559 |
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