Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity
نویسندگان
چکیده
منابع مشابه
Thick metric spaces , relative hyperbolicity , and quasi - isometric rigidity
We study the geometry of non-relatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with non-relatively hyperbolic peripheral subgroups is a quasi-isometry invariant...
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In this paper we introduce a quasi-isometric invariant class of metric spaces which we call metrically thick. We show that any metrically thick space is not (strongly) relatively hyperbolic with respect to any non-trivial collection of subsets. Further, we show that the property of being (strongly) relatively hyperbolic with thick peripheral subgroups is a quasi-isometry invariant. We show that...
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We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with nonrelatively hyperbolic peripheral subgroups is a quasi-isometry invariant. ...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2008
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-008-0317-1