Rigidity of convex co-compact diagonal actions

2024/08/06 by Subhadip Dey, Beibei Liu, Dey, Subhadip +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2408.03462

Abstract

Kleiner-Leeb and Quint showed that convex subsets in higher-rank symmetric spaces are very rigid compared to rank 1 symmetric spaces. Motivated by this, we consider convex subsets in products of proper CAT(0) spaces X₁× X₂ and show that for any two convex co-compact actions ρ_i(Γ) on X_i, where i=1, 2, if the diagonal action of Γ on X₁× X₂ via ρ=(ρ₁, ρ₂) is also convex co-compact, then under a suitable condition, ρ₁(Γ) and ρ₂(Γ) have the same marked length spectrum.

Related

• Compactification of a diagonal action on the product of CAT(-1) spaces
• Rigidity of compact rank one symmetric spaces
• Actions on products of CAT(-1) spaces
• CAT(0) spaces of higher rank II
• CAT(0) spaces of higher rank