Quasi-Mobius Homeomorphisms of Morse boundaries

Ruth Charney; Matthew Cordes; Devin Murray

doi:10.1112/blms.12246

Quasi-Mobius Homeomorphisms of Morse boundaries

Ruth Charney, Matthew Cordes, Devin Murray

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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 (Formula presented.) 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.

Original language	English
Pages (from-to)	501-515
Number of pages	15
Journal	Bulletin of the London Mathematical Society
Volume	51
Issue number	3
DOIs	https://doi.org/10.1112/blms.12246
Publication status	Published - Jun 2019

ASJC Scopus subject areas

General Mathematics

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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 (Formula presented.) 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.",

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Quasi-Mobius Homeomorphisms of Morse boundaries

Abstract

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