Cocycle superrigidity for median spaces of finite rank

2025/06/23 by Ma, Biao, Messaci, Lamine
#37B05 #51F99 #57S30 #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2506.19043

Abstract

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank, the superrigidity of Isom(X)-valued cocycles for a product of locally compact second countable groups. In the case of actions by irreducible lattices in such product groups, this approach yields a novel proof of the superrigidity of homomorphisms.

Citations

• Compact Median Algebras are μ-Boundaries in a unique way
• Isometric actions on locally compact finite rank median spaces
• Hyperbolic actions of higher-rank lattices come from rank-one factors
• Convex cores for actions on finite-rank median algebras
• Median geometry for spaces with measured walls and for groups
• Poc Sets, Median Algebras and Group Actions
• The Furstenberg Poisson Boundary and CAT(0) Cube Complexes
• Boundaries, rigidity of representations, and Lyapunov exponents
• Boundaries, Weyl groups, and Superrigidity
• The Poisson boundary of CAT(0) cube complex groups
• Kazhdan and Haagerup properties from the median viewpoint
• Superrigidity, generalized harmonic maps and uniformly convex spaces
• Superrigidity, Weyl groups, and actions on the Circle

Related

• Cocycle Superrigidity for Profinite Actions of Property (T) Groups
• On the Superrigidity of Malleable Actions with Spectral Gap
• Superrigidity, Weyl groups, and actions on the Circle
• On Popa's Cocycle Superrigidity Theorem
• Cocycle superrigidity for coinduced actions