Iteration of mapping classes and limits of hyperbolic 3-manifolds

Inventiones Mathematicae

Volumn 143, Issue 3, 2001, Pages 523-570

  Brock, Jeffrey F ^a,b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035579102     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005799     Document Type: Article

References (49)

1. S. Bleiler, A. Casson. Automorphisms of Surfaces After Neilsen and Thurston, volume 9. London Mathematical Society Student Texts, 1988
2. J. Anderson, R. Canary. Cores of hyperbolic 3-manifolds and limits of Kleinian groups. Amer. J. Math. 118 (1996), 745-779
3. R. Benedetti, C. Petronio. Lectures on Hyperbolic Geometry. Springer-Verlag, 1992
4. L. Bers. Simultaneous uniformization. Bull. AMS 66 (1960), 94-97
5. L. Bers. On boundaries of Teichmüller spaces and on kleinian groups: I. Annals of Math. 91 (1970), 570-600
6. L. Bers. An extremal problem for quasiconformal maps and a theorem by Thurston. Acta Math. 141 (1978), 73-98
7. L. Bers. On iterates of hyperbolic transformations of Teichmüller space. Amer. J. Math. 105 (1983), 1-11
8. J.S. Birman, A. Lubotzky, J. McCarthy. Abelian and solvable subgroups of the mapping class group. Duke Math. J. 50 (1983), 1107-1120
9. F. Bonahon. Bouts des variétés hyperboliques de dimension 3. Annals of Math. 124 (1986), 71-158
10. F. Bonahon. The geometry of Teichmüller space via geodesic currents. Invent. math. 92 (1988), 139-162
11. F. Bonahon. Shearing hyperbolic surfaces, bending pleated surfaces, and Thurston's symplectic form. Ann. Fac. Sci. Toulouse Math. 5 (1996), 233-297
12. F. Bonahon, J.P. Otal. Variétés hyperboliques à géodésiques arbitrairement courtes. Bull. London Math. Soc. 20 (1988), 255-261
13. J. Brock. Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds. In: Lipa's legacy (New York, 1995), pp. 81-106. Amer. Math. Soc., Providence, RI, 1997
14. J. Brock. Continuity of Thurston's length function. Geom. & Funct. Anal. 10 (2000), 741-797
15. J. Brock. Iteration of mapping classes and limits of hyperbolic 3-manifolds. Ph.D. Thesis, U.C. Berkeley, 1997
16. P. Buser. Geometry and Spectra of Compact Riemann Surfaces. Birkhauser Boston, 1992
17. R.D. Canary. Algebraic convergence of Schottky groups. Trans. AMS 337 (1994), 235-258
18. R.D. Canary. A covering theorem for hyperbolic 3-manifolds and its applications. Topology 35 (1996), 751-778
19. R.D. Canary, D.B.A. Epstein, P. Green. Notes on notes of Thurston. In: Analytical and Geometric Aspects of Hyperbolic Space, pp. 3-92. Cambridge University Press, 1987
20. J.W. Cannon, W. P. Thurston. Group invariant Peano curves. Preprint
21. P. Duren. Univalent Functions. Springer-Verlag, 1983
22. D.B.A. Epstein, A. Marden. Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces. In: Analytical and Geometric Aspects of Hyperbolic Space, pp. 113-254. Cambridge University Press, 1987
23. A. Fathi, R Laudenbach, V Poénaru. Travaux de Thurston sur les surfaces, volume 66-67. Astérisque, 1979
24. F. Gardiner. Teichmüller Theory and Quadratic Differentials. Wiley Interscience, 1987
25. L. Greenberg. Finiteness Theorems for Fuchsian and Kleinian Groups. In: Discrete Groups and Automorphic Functions, pp. 199-257. Academic Press, 1977
26. J.G. Hocking, G.S. Young. Topology. Addison-Wesley, 1961
27. N.V Ivanov. Subgroups of Teichmüller Modular Groups. AMS Translations of Mathematical Monographs, Vol. 115 (1992)
28. S. Kerckhoff, W. Thurston. Non-continuity of the action of the modular group at Bers' boundary of Teichmüller space. Invent, math. 100 (1990), 25-48
29. I. Kra. On spaces of Kleinian groups. Comment. Math. Helv. 47 (1972), 53-69
30. O. Lehto, K.J. Virtanen. Quasiconformal Mappings in the Plane. Springer-Verlag, 1973
31. A. Marden. The geometry of finitely generated kleinian groups. Annals of Math. 99 (1974), 383-462
32. B. Maskit. On boundaries of Teichmüller spaces and on kleinian groups: II. Annals of Math. 91 (1970), 607-639
33. B. Maskit. Kleinian Groups. Springer-Verlag, 1988
34. D. McCullough. Compact submanifolds of 3-manifolds with boundary. Quart. J. Math. Oxford 37 (1986), 299-307
35. C. McMullen. Iteration on Teichmüller space. Invent, math. 99 (1990), 425-454
36. C. McMullen. Renormalization and 3-Manifolds Which Fiber Over the Circle. Annals of Math. Studies 142, Princeton University Press, 1996
37. Y. Minsky. On rigidity, limit sets, and end invariants of hyperbolic 3-manifolds. J. of the AMS 2 (1994), 539-588
38. J. Morgan. On Thurston's uniformization theorem for three dimensional manifolds. In: The Smith Conjecture, pp. 37-125. Academic Press, 1984
39. J.P. Otal. Le théorème d'hyperbolisation pour les variétés flbrées de dimension trois. Astérisque, 1996
40. J.P. Otal. Thurston's hyperbolization of Haken manifolds. In: Surveys in differential geometry, Vol. III, pp. 77-194. Int. Press, 1996
41. T. Jørgensen, A. Marden. Algebraic and geometric convergence of kleinian groups. Math. Scand. 66 (1990), 47-72
42. P. Scott. Compact submanifolds of 3-manifolds. J. London Math. Soc. (2) 7 (1973), 246-250
43. J. Stallings. On fibering certain 3-manifolds. In: Topology of 3-manifolds, pp. 95-100. Prentice Hall, 1962
44. 1. Sem. Bourbaki 554 (1979/80)
45. D. Sullivan. On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. In: Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference. Annals of Math. Studies 97, Princeton, 1981
46. W.P. Thurston. Geometry and Topology of Three-Manifolds. Princeton lecture notes, 1979
47. W.P. Thurston. Hyperbolic structures on 3-manifolds I: Deformations of acylindrical manifolds. Annals of Math. 124 (1986), 203-246
48. W.P. Thurston. On the geometry and dynamics of diffeomorphisms of surfaces. Bull. AMS 19 (1988), 417-432
49. W.P. Thurston. Hyperbolic structures on 3-manifolds II: Surface groups and 3-manifolds which fiber over the circle. Preprint, 1986