Quasiconvexity in relatively hyperbolic groups
نویسندگان
چکیده
منابع مشابه
Relatively hyperbolic Groups
In this paper we develop some of the foundations of the theory of relatively hyperbolic groups as originally formulated by Gromov. We prove the equivalence of two definitions of this notion. One is essentially that of a group admitting a properly discontinuous geometrically finite action on a proper hyperbolic space, that is, such that every limit point is either a conical limit point or a boun...
متن کاملGrowth of relatively hyperbolic groups
We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth. Mathematics Subject Classification(2000). 20F65.
متن کاملLimit Groups for Relatively Hyperbolic
We begin the investigation of Γ-limit groups, where Γ is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of [16], we adapt the results from [21] and [22] to this context. Specifically, given a finitely generated group G, and a sequence of pairwise non-conjugate homomorphisms {hn : G → Γ}, we extract anR-tree with a nontrivial isomet...
متن کاملEndomorphisms of Relatively Hyperbolic Groups
We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. • If G is a non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. • If H is a non-parabolic subgroup of a relatively hyperb...
متن کاملQuasiconvexity of subsurface groups in hyperbolic 3-manifolds
Let Σ be a closed orientable surface of genus g ≥ 2. Suppose that Γ = π1(Σ) acts properly discontinuously on H by orientation preserving isometries. The quotient, M = H/Γ is a complete hyperbolic 3-manifold with a natural homotopy equivalence to Σ. In fact, by tameness [Bon], we know that M is homeomorphic to Σ×R. The proof of the Ending Lamination Conjecture [Mi1,BrCM] has lead to a reasonably...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2016
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2015-0029