Sublinearly Morse Boundary of CAT(0) admissible groups

TL;DR

This paper demonstrates that admissible groups acting on CAT(0) spaces are hierarchically hyperbolic and that their sublinearly-Morse boundary models Poisson boundaries, linking geometric group theory and boundary theory.

Contribution

It establishes the hierarchical hyperbolicity of admissible groups acting on CAT(0) spaces and connects their sublinearly-Morse boundary to Poisson boundaries.

Findings

Admissible groups acting on CAT(0) spaces are hierarchically hyperbolic.

Sublinearly-Morse boundary models Poisson boundaries under mild assumptions.

Provides a topological framework linking geometric and probabilistic boundaries.

Abstract

We show that if G is an admissible group acting geometrically on a CAT(0) space X, then G is a hierarchically hyperbolic space and with mild assumptions the sublinearly-Morse boundary of the group is a topological model for associated Poisson boundaries .