preprint
Inserted: 29 jun 2021
Last Updated: 24 may 2023
Year: 2021
Abstract:
We prove that a non-elementary measurable cocycle in the isometry group of a CAT(0)-space of finite telescopic dimension admits a Furstenberg map. We also show that a maximal cocycle $\sigma:\Gamma \times X \rightarrow \text{PU}(p,\infty)$ where $\Gamma < \text{PU}(1,n)$ is a torsion-free lattice and $(X,\mu_X)$ is a ergodic standard Borel $\Gamma$-space is finitely reducible. As a consequence, we prove an infinite dimensional rigidity phenomenon for cocycles.