Abstract
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.
-
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@incollection {abikoff:survey, MRKEY = {957510},
AUTHOR = {Abikoff, William},
TITLE = {Kleinian Groups---Geometrically Finite and Geometrically Perverse},
BOOKTITLE = {Geometry of Group Representations ({B}oulder, {\rm CO},
1987)},
SERIES = {Contemp. Math.},
NUMBER = {74},
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PUBLISHER = {Amer. Math. Soc.},
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} -
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@unpublished{agol:tame,
author={Agol, I.},
TITLE={Tameness of hyperbolic 3-manifolds, preprint},
YEAR={2004},
NOTE={arXiv:math.GT/0405568},
} -
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@article {ahlfors-bers, MRKEY = {0115006},
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@article {ahlfors:finitegen, MRKEY = {0167618},
AUTHOR = {Ahlfors, Lars V.},
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AUTHOR = {Alonso, J. M. and et al.},
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author={Bers, Lipman},
TITLE={Spaces of {K}leinian groups},
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SERIES={Ann. of Math. Studies},
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ADDRESS = {Princeton, NJ},
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MRNUMBER={0780038}
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@unpublished{brock-canary-minsky:ELCII,
author={Brooks, Robert and Canary, Richard D and Minsky, Yair N.},
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NOTE={arXiv:math.GT/0412006},
} \marginpar{Check} -
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AUTHOR = {Canary, R. D. and Epstein, D. B. A. and Green, P.},
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AUTHOR={Ghys, E. and de la Harpe ({\rm eds.}), P.},
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author={Gromov, G.},
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} -
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AUTHOR = {Harvey, W. J.},
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author={Klarreich, E.},
TITLE={The boundary at infinity of the curve complex and the relative {Teichmüller} space, preprint},
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FJOURNAL = {Commentarii Mathematici Helvetici},
VOLUME = {47},
YEAR = {1972},
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[marden:geometry]
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[mmcomplextwo]
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[minsky:taniguchi] Y. N. Minsky, "A geometric approach to the complex of curves on a surface," in Topology and Teichmüller Spaces (Katinkulta, 1995), World Sci. Publ., River Edge, NJ, 1996, pp. 149-158.
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AUTHOR = {Minsky, Yair N.},
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PAGES = {149--158},
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[minsky:torus]
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[minsky:kgcc]
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[minsky:boundgeom]
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} -
[minsky:warwick] Kleinian Groups and Hyperbolic 3-ManifoldsCambridge: Cambridge Univ. Press, 2003.
@proceedings {minsky:warwick, MRKEY = {2044542},
TITLE = {Kleinian Groups and Hyperbolic 3-Manifolds},
SERIES = {London Math. Soc. Lecture Note Ser.},
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EDITOR = {Komori, Y. and Markovic, V. and Series, C.},
ADDRESS = {Cambridge},
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} -
[moore:planetop]
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[scott:core]
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} \marginpar{Check} -
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AUTHOR = {Sullivan, Dennis},
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[wpt:II] Thurston, William P., Hyperbolic structures on 3-manifolds, II: surface groups and manifolds which fiber over the circle, preprint.
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[wpt:notes] Thurston, William P., The geometry and topology of 3-manifolds, 1982.
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[wpt:bull]
W. P. Thurston, "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry," Bull. Amer. Math. Soc., vol. 6, iss. 3, pp. 357-381, 1982.
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[wpt:I]
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[waterman:inequality]
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}