Bulletin (New Series) of the American Mathematical Society

Three dimensional manifolds, Kleinian groups and hyperbolic geometry

William P. Thurston

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.), Volume 6, Number 3 (1982), 357-381.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183548782

Mathematical Reviews number (MathSciNet)
MR648524

Zentralblatt MATH identifier
0496.57005

Subjects
Primary: 57M99: None of the above, but in this section 30F40: Kleinian groups [See also 20H10] 57S30: Discontinuous groups of transformations
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]

Citation

Thurston, William P. Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357--381. https://projecteuclid.org/euclid.bams/1183548782


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References

  • [Bers] L. Bers, Finite dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 131-172.
  • [Can, Th] J. Cannon and W. Thurston, Sphere-filling curves and limit sets of Kleinian groups (to appear).
  • [C, J, S] M. Culler, W. Jaco and H. Rubinstein, Incompressible surfaces in once-punctured torus bundles (to appear).
  • [F, H] W. Floyd and A. Hatcher, Incompressible surfaces in 2-bridge link complements (to appear).
  • [F, L, P] A. Fathi, F. Laudenbach, V. Poénaru et al., Travaus de Thurston sur les surfaces, Astérisque 66-67, Société Mathématique de France, 1979.
  • [Hak] W. Haken, Theorie der Normal Flachen, Acta Math. 105 (1961), 5.
  • [Hat] A. Hatcher, Incompressible surfaces in once-punctured torus bundles (to appear).
  • [H, T] A. Hatcher and W. Thurston, Incompressible surfaces in 2-bridge knot complements, Invent. Math, (to appear).
  • [Ja, Sh] W. H. Jaco and P. B. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. No. 2(1979).
  • [Joh] K. Johannson, Homotopy equivalence of 3-manifolds with boundaries, Lecture Notes in Math., no. 7761, Springer-Verlag, Berlin, Heidelberg, New York, 1979.
  • [M, Y] W. Meeks and S-T Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. 112 (1980), 441-484.
  • [Mey] R. Meyerhoff, The Chern-Simons invariant for hyperbolic 3-manifolds, thesis, Princeton University, 1981.
  • [Mil 1] J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7.
  • [Mil 2] J. Milnor, Hyperbolic geometry: the first 150 years, proceedings.
  • [Mos 1] G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. Math. Studies, No. 78, Princeton Univ. Press, Princeton, N.J., 1973.
  • [Mos 2] G. D. Mostow, Inst. Hautes Études Sci. Publ. Math.
  • [Poin] H. Poincaré, Cinquième complèment a l'analysis situs, Rend. Circ. Mat. Palermo 18 (1904), 45-110, or Oeuvres, t. VI, pp. 435-498.
  • [Pras] G. Prasad, Strong rigidity of Q-rank 1 lattices, Invent. Math., 5-6.
  • [Ril] R. Riley, Discrete parabolic representations of link groups, Mathematika 22 (1975), 141-150.
  • [Seif] H. Seifert, Topologie drei dimensionales gefasertei Raume, Acta Math. 60 (1933), 147-288.
  • [Smi] Proceedings of the Smith Conjecture Conference at Columbia University, (to appear).
  • [Sta] J. Stallings, On fibering certain-3-manifolds, Prentice-Hall, Engelwood Cliffs, N.J., 1962, pp. 95-100.
  • [Sul 1] D. Sullivan, Discrete conformal groups and measurable dynamics, these proceedings.
  • [Sul 2] D. Sullivan,
  • [Th 1] W. Thurston, The geometry and topology of 3-manifolds, preprint, Princeton Univ. Press (to appear).
  • [Th 2] W. Thurston, Hyperbolic structures on 3-manifolds, I: deformations of acylindrical manifolds, preprint.
  • [Th 3] W. Thurston, Hyperbolic structures on 3-manifolds, II: surface groups and 3-manifolds which fiber over the circle.
  • [Th 4] W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, I, preprint.
  • [Wal] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88.