Groups Quasi-isometric to Complex Hyperbolic Space
نویسنده
چکیده
We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.
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...
متن کاملar X iv : m at h / 05 12 59 2 v 4 [ m at h . G T ] 1 J ul 2 00 6 THICK METRIC SPACES , RELATIVE HYPERBOLICITY , AND QUASI - ISOMETRIC RIGIDITY
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. ...
متن کاملRigidity of quasi-isometries for symmetric spaces and Euclidean buildings
for all x ∈ X . Quasi-isometries occur naturally in the study of the geometry of discrete groups since the length spaces on which a given finitely generated group acts cocompactly and properly discontinuously by isometries are quasi-isometric to one another [Gro]. Quasi-isometries also play a crucial role in Mostow’s proof of his rigidity theorem: the theorem is proved by showing that equivaria...
متن کاملHyperbolic extensions of free groups
Given a finitely generated subgroup Γ≤ Out(F) of the outer automorphism group of the rank r free group F = Fr, there is a corresponding free group extension 1→ F→ EΓ→ Γ→ 1. We give sufficient conditions for when the extension EΓ is hyperbolic. In particular, we show that if all infinite order elements of Γ are atoroidal and the action of Γ on the free factor complex of F has a quasi-isometric o...
متن کاملJ an 2 00 6 THICK METRIC SPACES , RELATIVE HYPERBOLICITY , AND QUASI - ISOMETRIC RIGIDITY
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...
متن کامل