Furstenberg Maps For CAT(0) Targets Of Finite Telescopic Dimension

Abstract

We consider actions of locally compact groups $G$ on certain CAT(0) spaces $X$ by isometries. The CAT(0) spaces we consider have finite dimension at large scale. In case $B$ is a $G$-boundary, that is a measurable $G$-space with amenability and ergodicity properties, we prove the existence of equivariant maps from $B$ to the visual boundary $\partial X$.

16 pages, 1 figure

References in corpus (2)

• Boundaries, rigidity of representations, and Lyapunov exponents
• Algebraic Representations of Ergodic Actions and Super-Rigidity

Cited by in corpus (2)

• Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
• Isometric group actions with vanishing rate of escape on CAT(0) spaces