Contracting boundaries of CAT(0) spaces

As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well‐defined since quasi‐isometric CAT(0) spaces can have non‐homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the contracting boundary, made up of rays satisfying one of five hy...

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Bibliographic Details
Published in:Journal of topology 2015-03, Vol.8 (1), p.93-117
Main Authors: Charney, Ruth, Sultan, Harold
Format: Article
Language:English
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Summary:As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well‐defined since quasi‐isometric CAT(0) spaces can have non‐homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the contracting boundary, made up of rays satisfying one of five hyperbolic‐like properties. We prove that these properties are all equivalent and that the contracting boundary is a quasi‐isometry invariant. We use this invariant to distinguish the quasi‐isometry classes of certain right‐angled Coxeter groups.
ISSN:1753-8416
1753-8424
DOI:10.1112/jtopol/jtu017