Conical limit points and the Cannon-Thurston map
نویسندگان
چکیده
منابع مشابه
Conical Limit Points and the Cannon-thurston Map
Let G be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space Z so that there exists a continuous G-equivariant map i : ∂G → Z, which we call a Cannon-Thurston map. We obtain two characterizations (a dynamical one and a geometric one) of conical limit points in Z in terms of their pre-images under the CannonThurston map i. As an application we prove...
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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...
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This is an expository paper. We prove the Cannon-Thurston property for bounded geometry surface groups with or without punctures. We prove three theorems, due to Cannon-Thurston, Minsky and Bowditch. The proofs are culled out of earlier work of the author. AMS subject classification = 20F32, 57M50
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, and, in com...
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...
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ژورنال
عنوان ژورنال: Conformal Geometry and Dynamics of the American Mathematical Society
سال: 2016
ISSN: 1088-4173
DOI: 10.1090/ecgd/294