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Are geodesic metric spaces determined by their Morse boundaries?

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NPC - Non-positive curvature group actions and cohomology

Boundaries of hyperbolic spaces have played a key role in low dimensional topology and geometric group theory. In 1993, Paulin showed that the topology of the boundary of a hyperbolic space, together with its quasi-mobius structure, determines the space up to quasi-isometry. One can define an analogous boundary, called the Morse boundary, for any proper geodesic metric space. I will discuss an analogue of Paulin’s theorem for Morse boundaries of CAT spaces.   (Joint work with Devin Murray)



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