论文标题
旋转等效性和共生超级汇率
Rotation equivalence and cocycle superrigidity
论文作者
论文摘要
我们从描述性集合理论的角度分析了较高维度和由理性旋转群体引起的相应轨道等效关系的欧几里得球体。事实证明，这种等价关系在大于$ 2 $的维度上不可树。然后，我们证明了尺寸$ n \ geq 5 $中的旋转等价关系并不是任何较低维度中的borel borel。我们的方法结合了Furman和Ioana的作品与Margulis的$ S $ arithmetic基团的Superrigities定理相结合的。我们还应用技术来提供几何证据，证明存在许多成对无与伦比的等效关系，直到可降低了鲍尔的性关系。
We analyze Euclidean spheres in higher dimensions and the corresponding orbit equivalence relations induced by the group of rational rotations from the viewpoint of descriptive set theory. It turns out that such equivalence relations are not treeable in dimension greater than $2$. Then we show that the rotation equivalence relation in dimension $n \geq 5$ is not Borel reducible to the one in any lower dimension. Our methods combine a cocycle superrigidity result from the works of Furman and Ioana with the superrigidity theorem for $S$-arithmetic groups of Margulis. We also apply our techniques to give a geometric proof of the existence of uncountably many pairwise incomparable equivalence relations up to Borel reducibility.
