Real analytic SL(n,ℝ)-actions on closed manifolds

2025/08/06 by Son, Miri
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2508.04499

Abstract

We classify real-analytic SL(n,ℝ)-actions on closed manifolds of dimension m for 3≤ n≤ m≤2n-3, which extends Fisher--Melnick's work for SL(n,ℝ)-actions on closed n-manifolds. Additionally, we classify smooth SL(n,ℝ)-actions on closed m-manifolds that are fixed-point free. As a corollary, we obtain the density or non-density of structural stability of fixed-point free SL(n,ℝ)-actions.

Citations

• Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors
• Zimmer's conjecture for non-uniform lattices: escape of mass and growth of cocycles
• Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)
• Groups acting on manifolds: around the Zimmer program

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