Hyperbolic Structures on 3-manifolds, Ii: Surface Groups and 3-manifolds Which Fiber over the Circle

@inproceedings{Thurston2008HyperbolicSO,
  title={Hyperbolic Structures on 3-manifolds, Ii: Surface Groups and 3-manifolds Which Fiber over the Circle},
  author={William P. Thurston},
  year={2008}
}
The main result (0.1) of this paper is that every atoroidal three-manifold that fibers over the circle has a hyperbolic structure. Consequently, every fibered three-manifold admits a geometric decomposition. The main tool for constructing hyperbolic structures on fibered three-manifolds is the double limit theorem (4.1), which is of interest for its own sake and lays out general conditions under which sequences of quasi-Fuchsian groups have algebraically convergent subsequences. The main tool… CONTINUE READING
Highly Cited
This paper has 43 citations. REVIEW CITATIONS
34 Citations
34 References
Similar Papers

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 34 references

In Geometric dynamics (Rio de Janeiro

  • Dennis Sullivan. Conformal dynamical systems
  • 1981), volume 1007 of Lecture Notes in Math…
  • 1983
Highly Influential
5 Excerpts

Three-manifolds, foliations and circles, I, 1997, math.GT/9712268

  • William P. Thurston
  • 1997

Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3

  • Jean-Pierre Otal
  • Astérisque, (235):x+159,
  • 1996
2 Excerpts

Minsky . On rigidity , limit sets , and end invariants of hyperbolic 3 - manifolds

  • N. Yair
  • Renormalization and 3 - manifolds which fiber…
  • 1996

Renormalization and 3-manifolds which fiber over the circle

  • Curtis T. McMullen
  • volume 142 of Annals of Mathematics Studies…
  • 1996
2 Excerpts

Subgroups of surface groups are almost geometric

  • Peter Scott.
  • Astérisque
  • 1996

limit sets

  • Yair N. Minsky. On rigidity
  • and end invariants of hyperbolic 3-manifolds. J…
  • 1994
1 Excerpt

Asymptotic properties of depth one foliations in hyperbolic 3-manifolds

  • Sérgio R. Fenley
  • J. Differential Geom., 36(2):269–313,
  • 1992
1 Excerpt

Fenley . Asymptotic properties of depth one foliations in hyperbolic 3 - manifolds

  • R. Sérgio
  • J . Differential Geom .
  • 1992

volume 9 of London Mathematical Society Student Texts

  • Andrew J. Casson, Steven A. Bleiler. Automorphisms of surfaces after Nielsen, Thurston
  • Cambridge University Press, Cambridge,
  • 1988
1 Excerpt

Similar Papers

Loading similar papers…