2018/01/14 by Ruth Charney, Matthew Cordes, Devin Murray · 13 citations
Mathematics · #Analytic and geometric function theory #Boundary (topology) #Converse #Geodesic #Geometric and Algebraic Topology #Homeomorphism (graph theory) #Mathematical Dynamics and Fractals #Metric (unit) #Metric space #Morse code #math.GR #math.GT #msc:20F65 #msc:57M07
paper · pdf · doi:10.1112/blms.12246
published in Bulletin of the London Mathematical Society 51(3), 501-515 (Wiley) · arXiv admin note: substantial text overlap with arXiv:1707.07028
arxiv created 2018/01/14 · openalex created_date 2018/01/26 · openalex publication_date 2019/03/24 · arxiv updated 2019/04/03 · openalex updated_date 2026/08/06
The Morse boundary of a proper geodesic metric space is designed to encode hypberbolic-like behavior in the space. A key property of this boundary is that a quasi-isometry between two such spaces induces a homeomorphism on their Morse boundaries. In this paper, we investigate when the converse holds. We prove that for X,Y proper, cocompact spaces, a homeomorphism between their Morse boundaries is induced by a quasi-isometry if and only if the homeomorphism is quasi-mobius and 2-stable.