Contracting Boundaries of CAT(0) Spaces

Ruth Charney; Harold Sultan

doi:10.1112/jtopol/jtu017

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arXiv · 1308.6615

Contracting Boundaries of CAT(0) Spaces

Ruth Charney·Harold Sultan

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Abstract

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 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.

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Ruth Charney, Harold Sultan. 2013-08-29. Contracting Boundaries of CAT(0) Spaces. https://doi.org/10.1112/jtopol%2Fjtu017

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