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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| Published in | Journal of topology Vol. 8; no. 1; pp. 93 - 117 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford University Press
01.03.2015
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| Online Access | Get full text |
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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. |
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| Bibliography: | 2010 Mathematics Subject Classification 20F65, 20F67 (primary), 20F55 (secondary). R. Charney was partially supported by NSF grant DMS‐1106726. |
| ISSN: | 1753-8416 1753-8424 |
| DOI: | 10.1112/jtopol/jtu017 |