The classification of Kleinian surface groups, I: models and bounds

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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      JOURNAL = {Proc. Amer. Math. Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
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      YEAR = {1994},
      NUMBER = {1},
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      MRCLASS = {30F40 (20H10 22E40)},
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  • [masur-minsky:complex1] Go to document H. A. Masur and Y. N. Minsky, "Geometry of the complex of curves. I. Hyperbolicity," Invent. Math., vol. 138, iss. 1, pp. 103-149, 1999.
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      TITLE = {Geometry of the complex of curves. {II}. {H}ierarchical structure},
      JOURNAL = {Geom. Funct. Anal.},
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      ISSN = {1016-443X},
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      author={Thurston, William P.},
      TITLE={Hyperbolic structures on 3-manifolds, {II}: surface groups and manifolds which fiber over the circle, preprint},
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      author={Thurston, William P.},
      TITLE={The geometry and topology of 3-manifolds},
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      TITLE = {Three-dimensional manifolds, {K}leinian groups and hyperbolic geometry},
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      MRNUMBER = {83h:57019},
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      ZBLNUMBER = {0496.57005},
      }
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      AUTHOR = {Thurston, William P.},
      TITLE = {Hyperbolic structures on {$3$}-manifolds. {I}. {D}eformation of acylindrical manifolds},
      JOURNAL = {Ann. of Math.},
      FJOURNAL = {Annals of Mathematics. Second Series},
      VOLUME = {124},
      YEAR = {1986},
      NUMBER = {2},
      PAGES = {203--246},
      ISSN = {0003-486X},
      CODEN = {ANMAAH},
      MRCLASS = {57N10},
      MRNUMBER = {88g:57014},
      MRREVIEWER = {G. Peter Scott},
      DOI = {10.2307/1971277},
      ZBLNUMBER = {0668.57015},
      }
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    @book {wpt:textbook, MRKEY = {1435975},
      AUTHOR = {Thurston, William P.},
      TITLE = {Three-Dimensional Geometry and Topology. {V}ol. 1},
      SERIES = {Princeton Math. Series},
      NUMBER = {35},
      NOTE = {(Silvio Levy, ed.)},
      PUBLISHER = {Princeton Univ. Press},
      ADDRESS = {Princeton, NJ},
      YEAR = {1997},
      PAGES = {x+311},
      ISBN = {0-691-08304-5},
      MRCLASS = {57M50 (53A35 57M25 57M60 57N10)},
      MRNUMBER = {97m:57016},
      MRREVIEWER = {Athanase Papadopoulos},
      ZBLNUMBER = {0873.57001},
      }
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    @article {waterman:inequality, MRKEY = {1239454},
      AUTHOR = {Waterman, P. L.},
      TITLE = {Möbius transformations in several dimensions},
      JOURNAL = {Adv. Math.},
      FJOURNAL = {Advances in Mathematics},
      VOLUME = {101},
      YEAR = {1993},
      NUMBER = {1},
      PAGES = {87--113},
      ISSN = {0001-8708},
      CODEN = {ADMTA4},
      MRCLASS = {30F35 (51M10)},
      MRNUMBER = {95h:30056},
      ZBLNUMBER={0793.15019},
      DOI = {10.1006/aima.1993.1043},
      }

Authors

Yair Minsky

Department of Mathematics
Yale University
New Haven, CT 06520-8283
United States