Quasi-Mobius Homeomorphisms of Morse boundaries

14 Jan 2018  ·  Charney Ruth, Cordes Matthew, Murray Devin ·

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. read more

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Geometric Topology Group Theory