论文标题
Zimmer计划，用于部分双曲动作
The Zimmer Program for partially hyperbolic actions
论文作者
论文摘要
Zimmer在较高排名群中的超级滋养定理及其晶格启动了一项研究计划，旨在对半岛谎言组及其格子的行动进行分类，即被称为{\ IT Zimmer Programs}。当组相对于相空间的维度太大时，Zimmer猜想预测这些动作实际上都是微不足道的。在另一个极端情况下，当行动表现出足够的规则行为时，这些动作都应是代数的。 We make progress in the program by showing smooth conjugacy to a bi-homogeneous model (up to a finite cover) for volume-preserving actions of semisimple Lie groups without compact or rank one factors, which have two key assumptions: partial hyperbolicity for a large class of elements ({\it totally partial hyperbolicity}) and accessibility, a condition on the webs generated by dynamically-defined foliations.我们还获得了满足更强假设的高级阿贝尔群体的行动的分类。
Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, known as the {\it Zimmer program}. When the group is too large relative to the dimension of the phase space, the Zimmer conjecture predicts that the actions are all virtually trivial. At the other extreme, when the actions exhibit enough regular behavior, the actions should all be of algebraic origin. We make progress in the program by showing smooth conjugacy to a bi-homogeneous model (up to a finite cover) for volume-preserving actions of semisimple Lie groups without compact or rank one factors, which have two key assumptions: partial hyperbolicity for a large class of elements ({\it totally partial hyperbolicity}) and accessibility, a condition on the webs generated by dynamically-defined foliations. We also obtain classification for actions of higher-rank abelian groups satisfying stronger assumptions.
