Sublinearly Morse boundary I: CAT(0) spaces

To every Gromov hyperbolic space X one can associate a at infinity called the boundary of X. showed that quasi-isometries metric spaces induce homeomorphisms on their boundaries, thus giving rise to well-defined notion group. Croke and Kleiner visual non-positively curved (CAT(0)) groups is not well-defined, since quasi-isometric CAT(0) have non-homeomorphic boundaries. We attempt construct an analogue encodes directions in space. this end, for any sublinear function κ, we define subset κ–Morse boundary. show that, equipped with coarse topology, QI-invariant metrizable. That say, group well-defined. In case Right-angled Artin groups, it shown Appendix Poisson random walks naturally identified (tlog⁡t)–boundary.