2019/11/08 by Yulan Qing, Qing, Yulan, Abdul Zalloum +1
Mathematics · #20F65 #51F99 #FOS: Mathematics #Geometry and complex manifolds #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1911.03296
openalex publication_date 2019/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a sublinear function κ, κ-Morse boundaries \pka X of proper \CAT spaces are introduced by Qing, Rafi and Tiozzo. It is a topological space that consists of a large set of quasi-geodesic rays and it is quasi-isometrically invariant and metrizable. In this paper, we study the sublinearly Morse boundaries with the assumption that there is a proper cocompact action of a group G on the \CAT space in question. We show that G acts minimally on \pka G and that contracting elements of G induces a weak north-south dynamic on \pka G. Furthermore, we show that a homeomorphism f \from \pka G → \pka G' comes from a quasi-isometry if and only if f is successively quasi-möbius and stable. Lastly, we characterize exactly when the sublinearly Morse boundary of a \CAT space is compact.