التفاصيل البيبلوغرافية
| العنوان: |
Incomparable actions of free groups |
| المؤلفون: |
Conley, Clinton T., Miller, Benjamin D. |
| المصدر: |
Ergodic theory and dynamical systems 37 (7) (2017) 2084-2098 |
| سنة النشر: |
2020 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Logic, Mathematics - Dynamical Systems, 03E15, 28A05 (Primary), 22F10, 37A20 (Secondary) |
| الوصف: |
Suppose that $X$ is a Polish space, $E$ is a countable Borel equivalence relation on $X$, and $\mu$ is an $E$-invariant Borel probability measure on $X$. We consider the circumstances under which for every countable non-abelian free group $\Gamma$, there is a Borel sequence $(\cdot_r)_{r \in \mathbb{R}}$ of free actions of $\Gamma$ on $X$, generating subequivalence relations $E_r$ of $E$ with respect to which $\mu$ is ergodic, with the further property that $(E_r)_{r \in \mathbb{R}}$ is an increasing sequence of relations which are pairwise incomparable under $\mu$-reducibility. In particular, we show that if $E$ satisfies a natural separability condition, then this is the case as long as there exists a free Borel action of a countable non-abelian free group on $X$, generating a subequivalence relation of $E$ with respect to which $\mu$ is ergodic. |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.1017/etds.2016.11 |
| URL الوصول: |
http://arxiv.org/abs/2002.09651 |
| رقم الانضمام: |
edsarx.2002.09651 |
| قاعدة البيانات: |
arXiv |