2018/01/15 by Sarah C. Mousley, Mousley, Sarah C., Jacob A. Russell +2
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1801.04867
20 pages, 2 figures
arxiv created 2018/01/15 · openalex publication_date 2018/01/15 · arxiv updated 2018/01/16 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We generalize a result of Paulin on the Gromov boundary of hyperbolic groups to the Morse boundary of proper, maximal hierarchically hyperbolic spaces admitting cocompact group actions by isometries. Namely we show that if the Morse boundaries of two such spaces each contain at least three points, then the spaces are quasi-isometric if and only if there exists a 2-stable, quasi-möbius homeomorphism between their Morse boundaries. Our result extends a recent result of Charney-Murray, who prove such a classification for CAT(0) groups, and is new for mapping class groups and the fundamental groups of 3-manifolds without Nil or Sol components.