Cannon-Thurston maps for hyperbolic group extensions
نویسندگان
چکیده
منابع مشابه
Cannon–thurston Maps for Hyperbolic Free Group Extensions
This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free groups of finite rank at least 3 and consider a convex cocompact subgroup Γ ≤ Out(F), i.e. one for which the orbit map from Γ into the free factor complex of F is a quasi-isometric embedding. The subgroup Γ determines an extension EΓ of F, and t...
متن کاملRelative Hyperbolic Extensions of Groups and Cannon-thurston Maps
Let 1 → (K, K1) → (G, NG(K1)) → (Q, Q1) → 1 be a short exact sequence of pairs of finitely generated groups with K strongly hyperbolic relative to the subgroup K1. Let relative hyperbolic boundary of K with respect to K1 contains atleast three distinct parabolic end points and for all g ∈ G there exists k ∈ K such that gK1g −1 = kK1k , then we prove that there exists a quasi-isometric section s...
متن کاملCannon–thurston Maps for Kleinian Groups
We show that Cannon–Thurston maps exist for degenerate free groups without parabolics, that is, for handlebody groups. Combining these techniques with earlier work proving the existence of Cannon–Thurston maps for surface groups, we show that Cannon–Thurston maps exist for arbitrary finitely generated Kleinian groups without parabolics, proving conjectures of Thurston and McMullen. We also show...
متن کاملCannon–thurston Maps Do Not Always Exist
We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a continuous map of the boundaries. 2010 Mathematics Subject Classification: 20F67
متن کاملEnding Laminations and Cannon-Thurston Maps
In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian surface groups. In this paper we prove that pre-images of points are precisely end-points of leaves of the ending lamination whenever the Cannon-Thurston map is not one-to-one. In particular, the Cannon-Thurston map is finite-to-one. This completes the proof of the conjectural picture of Cannon-Thurston maps. In conjunct...
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: Topology
سال: 1998
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(97)00036-0