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Title:
Quasi-mobius maps between Morse boundaries of CAT(0) spaces
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The Morse boundary of a geodesic metric space is a topological space consisting of equivalence classes of geodesic rays satisfying a Morse condition. A key property of this boundary is quasi-isometry invariance: a quasi-isometry between two proper geodesic metric spaces induces a homeomorphism on their Morse boundaries. In the case of a hyperbolic metric space, the Morse boundary is the usual Gromov boundary and Paulin proved that this boundary, together with its quasi-mobius structure, determines the space up to quasi-isometry. I will discuss an analogue of Paulin’s theorem for Morse boundaries of CAT(0) spaces. This is joint work with Devin Murray.
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