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arXiv · 2002.02485

Rigidity theorems for higher rank lattice actions

Homin Lee
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Abstract

Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global rigidity of the $\Gamma$-action when $\Gamma$ 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.

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Homin Lee. 2020-02-06. Rigidity theorems for higher rank lattice actions. https://arxiv.org/abs/2002.02485

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