论文标题
高铁硼酸作用的共同体学
Cohomology of hyperfinite Borel actions
论文作者
论文摘要
我们研究了标准Borel空间$（x，\ Mathcal {b}）$的可数组的Cocycles $γ$的borel borel自动形态，以本地紧凑的第二可计数组$ g $中的值。我们证明，对于高铁组$γ$，同生的亚组在同伴组中密集。我们描述了$ 2 $ - 模块计的所有Borel Cocycles，并表明任何此类Cocycle均与Cocycle共同，并具有可计数的密集亚组$ h $ ok $ g $。我们还提供了Gottschalk-Hedlund定理的Borel版本。
We study cocycles of countable groups $Γ$ of Borel automorphisms of a standard Borel space $(X, \mathcal{B})$ taking values in a locally compact second countable group $G$. We prove that for a hyperfinite group $Γ$ the subgroup of coboundaries is dense in the group of cocycles. We describe all Borel cocycles of the $2$-odometer and show that any such cocycle is cohomologous to a cocycle with values in a countable dense subgroup $H$ of $G$. We also provide a Borel version of Gottschalk-Hedlund theorem.
