The topology of deformation spaces of Kleinian groups

Annals of Mathematics

Volumn 152, Issue 3, 2000, Pages 693-741

  Anderson, James W ^a   Canary, Richard D ^b   Mccullough, Darryl ^c  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034310137     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2661352     Document Type: Article

References (43)

1. W. ABIKOFF and B. MASKIT, Geometric decompositions of Kleinian groups, Amer. J. Math. 99 (1977), 687-697.
2. L. V. AHLFORS, The structure of a finitely generated Kleinian group, Acta Math. 122 (1969), 1-17.
3. J. W. ANDERSON and R. D. CANARY, Cores of hyperbolic 3-manifolds and limits of Kleinian groups, Amer. J. Math. 118 (1996), 745-779.
4. J. W. ANDERSON and R. D. CANARY, Algebraic limits of Kleinian groups which rearrange the pages of a book, Invent. Math. 126 (1996), 205-214.
5. J. W. ANDERSON, R. D. CANARY, M. CULLER, and P. SHALEN, Free Kleinian groups and volumes of hyperbolic 3-manifolds, J. Diff. Geom. 43 (1996), 738-782.
6. R. BENEDETTI and C. PETRONIO, Lectures on Hyperbolic Geometry, Universitext, Springer-Verlag, New York, 1992.
7. L. BERS, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. 91 (1970), 570-600.
8. F. BONAHON, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986), 71-158.
9. F. BONAHON and J. P. OTAL, Variétés hyperboliques à géodésiques arbitrairement courtes, Bull. London Math. Soc. 20 (1988), 255-261.
10. K. BROMBERG, Hyperbolic Dehn surgery on geometrically infinite 3-manifolds, preprint.
11. R. D. CANARY, A covering theorem for hyperbolic 3-manifolds and its applications, Topology 35 (1996), 751-778.
12. R. D. CANARY and D. McCuLLOUGH, Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups, preprint.
13. R. D. CANARY and Y. N. MINSKY, On limits of tame hyperbolic 3-manifolds, J. Diff. Geom. 43 (1996), 1-41.
14. T. D. COMAR, Hyperbolic Dehn surgery and convergence of Kleinian groups, Ph.D. thesis, University of Michigan, 1996.
15. J. Hempel, 3-manifolds, Ann. of Math. Studies, No. 86, Princeton Univ. Press, Princeton, NJ, 1976.
16. J. HOLT, Some new behaviour in the deformation theory of Kleinian groups, Comm. Anal. Geom., to appear.
17. W. HUREWICZ and H. WALLMAN, Dimension Theory, Princeton Math. Series 4, Princeton Univ. Press, Princeton, NJ, 1941.
18. W. JACO and P. B. SHALEN, Seifert Fibered Spaces in 3-Manifolds, Mem. A.M.S. 21 (1979), no. 221.
19. K. JOHANNSON, Homotopy Equivalences of 3-manifolds with Boundaries, Lecture Notes in Math. 761, Springer-Verlag, New York, 1979.
20. T. JØRGENSEN, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976), 739-749.
21. T. JØRGENSEN and A. MARDEN, Algebraic and geometric convergence of Kleinian groups, Math. Scand. 66 (1990), 47-72.
22. M. KAPOVICH, Hyperbolic Manifolds and Discrete Groups: Lectures on Thurston's Hyperbolization, Birkhäuser, 2000.
23. R. S. KULKARNI and P. B. SKALEN, On Ahlfors' finiteness theorem, Adv. Math. 76(1989), 155-169.
24. A. MARDEN, The geometry of finitely generated Kleinian groups, Ann. of Math. 99 (1974), 383-462.
25. B. MASKIT, On boundaries of Teichmüller spaces and on Kleinian groups II, Ann. of Math. 91 (1970), 607-639.
26. _, Kleinian Groups, Springer-Verlag, New York, 1988.
27. D. MCCULLOUGH, Compact submanifolds of 3-manifolds with boundary, Quart. J. Math. Oxford 37 (1986), 299-307.
28. D. MCCULLOUGH, A. MILLER, and G. A. SWARUP, Uniqueness of cores of noncompact 3-manifolds, J. London Math. Soc. 32 (1985), 548-556.
29. C. T. McMULLEN, Complex earthquakes and Teichmüller theory, J. A.M.S. 11 (1998), 283-320.
30. J. MILNOR, Periodic orbits, external rays, and the Mandelbrot set: an expository account (Orsay, 1995), Astérisque, No. 261 (2000), 277-333.
31. Y. N. MINSKY, On rigidity, limit sets and end invariants of hyperbolic 3-manifolds, J. A.M.S. 7 (1994), 539-588.
32. _, The classification of punctured-torus groups, Ann. of Math. 149(1999), 559-626.
33. J. W. MORGAN, On Thurston's uniformization theorem for three-dimensional manifolds, in The Smith Conjecture (J. Morgan and H. Bass, eds.), Academic Press, Orlando, FL, 1984, 37-125.
34. J. W. MORGAN and P. B. SKALEN, Degenerations of hyperbolic structures, III: Actions of 3-manifold groups on trees and Thurston's compactness theorem, Ann. of Math. 127 (1988), 457-519.
35. K. OHSHIKA, Ending laminations and boundaries for deformation spaces of Kleinian groups, J. London Math. Soc. 42 (1990), 111-121.
36. J.-P. OTAL, Thurston's hyperbolization of Haken manifolds, in Surveys in Differential Geometry, Vol. III, Internat. Press, Boston, MA 1998, 77-194.
37. G. P. SCOTT, Compact submanifolds of 3-manifolds, J. London Math. Soc. 7 (1973), 246-250.
38. D. SCHLEICHER, Rational parameter rays of the Mandelbrot set (Orsay, 1995), Astérisque, No. 261 (2000), 405-443.
39. D. P. SULLIVAN, Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. 122 (1985), 401-418.
40. _, Quasiconformal homeomorphisms and dynamics II. Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985), 243-260.
41. W. P. THURSTON, Three-dimensional manifolds, Kleinian groups, and hyperbolic geometry, Bull. A.M.S. 6 (1982), 357-381.
42. _, The Geometry and Topology of 3-Manifolds, Lecture Notes, Princeton Univ., Princeton, NJ, 1980.
43. G. W. WHITEHEAD, Elements of Homotopy Theory, Graduate Texts in Math. 61 (1978), Springer-Verlag, New York.