2022/06/08 by Enhui Shi, Hui Xu, Shi, Enhui +1
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2206.04022
openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the rigidity in the sense of Zimmer for higher rank lattice actions on dendrites and show that: (1) if Γ is a higher rank lattice and X is a nondegenerate dendrite with no infinite order points, then any action of Γ on X cannot be almost free; (2) if Γ is further a finite index subgroup of SLn(\mathbb Z) with n≥ 3, then every action of Γ on X has a nontrivial almost finite subsystem. During the proof, we get a new characterization of the left-orderability of a finitely generated group through its actions on dendrites.