2020/02/06 by Lee, Homin
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2002.02485
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.