The classification of Kleinian surface groups I : Models and bounds : preprint

By Yair N. Minsky. 2003

269 citations recorded by the source corpus.

We give the first part of a proof of Thurston’s Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a “Lipschitz model” for the thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a priori geometric bounds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4df0c88c27ea4e4260d172103b63268400e8ead5

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Shrinkwrapping and the taming of hyperbolic 3-manifolds : preprint (2004, methodology): “It also follows from [Ca] that the various results of §9 [Ca] hold for N. (5) Theorem 7.3 is the last step needed to prove the monumental classification theorem, the other parts being established by Alhfors, Bers, Kra, Marden, Maskit, Mostow, Prasad, Sullivan, Thurston, Minsky, Masur–Minsky, Brock–C”
Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups (2004, background): “5Minsky [95] and Brock-Canary-Minsky [24] have established the Ending Lamination Con-”
On hyperbolicity of free splitting and free factor complexes (2012, background): “Ending Lamination Conjecture [24], [27], [10] (see [26] for detailed background discussion about this solution).”
Cannon-Thurston Maps for Surface Groups (2006, methodology): “1 of [Min10]) A tight geodesic in H supported in a component domain of complexity 4 is called a 4-geodesic and an edge of a 4-geodesic in H is called a 4-edge.”
Realising end invariants by limits of minimally parabolic, geometrically finite groups (2005, unknown): “Once Marden’s conjecture is solved, to show that every (finitely generated and torsion-free) Kleinian group is a limit of quasi-conformal deformations of a geometrically finite group, using the resolution of the ending lamination conjecture by Brock-Canary-Minsky, what we need to do is to prove that”
A characterization of short curves of a Teichmuller geodesic (2004, background): “if the injectivity radius of N is positive, and we say g has bounded geometry if, for some ǫ > 0, the injectivity radius of the hyperbolic metric at g(t) is larger than ǫ. Using the technology developed in [8] an d [13] we prove:”
COMBINATORIAL RIGIDITY IN CURVE COMPLEXES AND MAPPING CLASS GROUPS (2005, background): “It was later to play a central role in the proof by Minsky, Brock and Canary of Thurston’s ending lamination conjecture [Brock et al. 2004].”
Quasiconvexity in the curve complex (2003, background): “G T ] 7 J ul 2 00 3 QUASICONVEXITY IN THE CURVE COMPLEX HOWARD MASUR AND YAIR MINSKY”
Asymptotics of Weil–Petersson Geodesics I: Ending Laminations, Recurrence, and Flows (2008, methodology): “We expect in general that the ending lamination should predict extensive information about bounded and short curves along the ray, in line with the ending lamination theorem of [BCM].”