2024/11/21 by Jinpeng An, Aaron Brown, An, Jinpeng +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2411.13858
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove many new cases of Zimmer's conjecture for actions by lattices in non-ℝ-split semisimple Lie groups G. By prior arguments, Zimmer's conjecture reduces to studying certain probability measures invariant under a minimal parabolic subgroup for the induced G-action. Two techniques are introduced to give lower bounds on the dimension of a manifold M admitting a non-isometric action. First, when the Levi component of the stabilizer of the measure has higher-rank simple factors, cocycle superrigidity provides a lower bound on the dimension of M. Second, when certain fiberwise coarse Lyapunov distributions are one-dimensional, a measure rigidity argument provides additional invariance of the measure if the associated root spaces are higher-dimensional.