A rank-one CAT(0) group is determined by its Morse boundary

Ruth Charney; Devin Murray

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arXiv · 1707.07028

A rank-one CAT(0) group is determined by its Morse boundary

Ruth Charney·Devin Murray

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Abstract

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 cocompact CAT(0) spaces, a homeomorphism of Morse boundaries is induced by a quasi-isometry if and only if the homeomorphism is quasi-mobius and 2-stable.

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Ruth Charney, Devin Murray. 2017-07-21. A rank-one CAT(0) group is determined by its Morse boundary. https://arxiv.org/abs/1707.07028

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