论文标题
高级晶格动作的刚性定理
Rigidity theorems for higher rank lattice actions
论文作者
论文摘要
让$γ$成为一个弱不可约的高级晶格。在本文中，根据Zimmer计划的理念，我们将证明$γ$的成果各种刚性结果。我们提供新的刚性结果，包括$γ$ Action的本地和全球刚度，当$γ$没有财产（t）时。新成分是动力学的超级基因定理。可以将其视为Zimmer的Cocycle超分性定理的概括，因为它在动态和代数上提供了几乎相同的后果。这使我们能够使用动力学超级符号而不是Zimmer的Cocycle超级基因定理得出各种刚度结果。
Let $Γ$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $Γ$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global rigidity of the $Γ$-action when $Γ$ does not have Property (T). The new ingredient is a dynamical cocycle super-rigidity theorem. It can be thought of as the generalization of Zimmer's cocycle super-rigidity theorem since it provides almost the same consequences dynamically and algebraically. This allows us to derive various our rigidity results using dynamical super-rigidity instead of Zimmer's cocycle super-rigidity theorem.
