Volume 16, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Deformation spaces of Kleinian surface groups are not locally connected

Aaron D Magid

Geometry & Topology 16 (2012) 1247–1320
Bibliography
1 W Abikoff, B Maskit, Geometric decompositions of Kleinian groups, Amer. J. Math. 99 (1977) 687 MR0480992
2 I Agol, Tameness of hyperbolic $3$–manifolds arXiv:math.GT/0405568
3 L Ahlfors, L Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. 72 (1960) 385 MR0115006
4 J W Anderson, R D Canary, Algebraic limits of Kleinian groups which rearrange the pages of a book, Invent. Math. 126 (1996) 205 MR1411128
5 J W Anderson, R D Canary, D McCullough, The topology of deformation spaces of Kleinian groups, Ann. of Math. 152 (2000) 693 MR1815699
6 R Benedetti, C Petronio, Lectures on hyperbolic geometry, Universitext, Springer (1992) MR1219310
7 L Bers, Spaces of Riemann surfaces as bounded domains, Bull. Amer. Math. Soc. 66 (1960) 98 MR0111835
8 L Bers, Spaces of Kleinian groups, from: "Several Complex Variables, I (Proc. Conf., Univ. of Maryland, College Park, MD, 1970)" (editor J Horváth), Springer (1970) 9 MR0271333
9 B H Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993) 245 MR1218098
10 J Brock, Boundaries of Teichmüller spaces and end-invariants for hyperbolic $3$–manifolds, Duke Math. J. 106 (2001) 527 MR1813235
11 J Brock, K Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
12 J Brock, K Bromberg, R D Canary, Y N Minsky, Local topology in deformation spaces of hyperbolic $3$–manifolds, Geom. Topol. 15 (2011) 1169 MR2831259
13 J Brock, K Bromberg, R Evans, J Souto, Tameness on the boundary and Ahlfors' measure conjecture, Publ. Math. Inst. Hautes Études Sci. (2003) 145 MR2031201
14 J Brock, R D Canary, Y N Minsky, The classification of finitely generated Kleinian groups, in preparation
15 J Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups, II: The ending lamination conjecture arXiv:math.GT/0412006
16 K Bromberg, Rigidity of hyperbolic $3$–manifolds with geometrically finite ends, PhD thesis, University of California, Berkeley (1998)
17 K Bromberg, Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives, J. Amer. Math. Soc. 17 (2004) 783 MR2083468
18 K Bromberg, Rigidity of geometrically finite hyperbolic cone-manifolds, Geom. Dedicata 105 (2004) 143 MR2057249
19 K Bromberg, Projective structures with degenerate holonomy and the Bers density conjecture, Ann. of Math. 166 (2007) 77 MR2342691
20 K Bromberg, The space of Kleinian punctured torus groups is not locally connected, Duke Math. J. 156 (2011) 387 MR2772066
21 K Bromberg, J Holt, Self-bumping of deformation spaces of hyperbolic $3$–manifolds, J. Differential Geom. 57 (2001) 47 MR1871491
22 K Bromberg, J Souto, The density conjecture: A prehistoric approach, in preparation
23 R Brooks, J P Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982) 163 MR650375
24 D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
25 R D Canary, Introductory bumponomics: the topology of deformation spaces of hyperbolic $3$–manifolds, from: "Teichmüller theory and moduli problem" (editors I Biswas, R S Kulkarni, S Mitra), Ramanujan Math. Soc. Lect. Notes Ser. 10, Ramanujan Math. Soc. (2010) 131 MR2667553
26 R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984)" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3 MR903850
27 R D Canary, D McCullough, Homotopy equivalences of $3$–manifolds and deformation theory of Kleinian groups, Amer. Math. Soc. (2004) MR2096234
28 V Chuckrow, On Schottky groups with applications to kleinian groups, Ann. of Math. 88 (1968) 47 MR0227403
29 M Culler, P B Shalen, Varieties of group representations and splittings of $3$–manifolds, Ann. of Math. 117 (1983) 109 MR683804
30 A Douady, J H Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. 18 (1985) 287 MR816367
31 R Evans, J Holt, Non-wrapping of hyperbolic interval bundles, Geom. Funct. Anal. 18 (2008) 98 MR2399097
32 W Heil, On the existence of incompressible surfaces in certain $3$–manifolds. II, Proc. Amer. Math. soc. 25 (1970) 429 MR0266222
33 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
34 C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. 162 (2005) 367 MR2178964
35 T Jørgensen, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976) 739 MR0427627
36 M Kapovich, Hyperbolic manifolds and discrete groups, Progress in Math. 183, Birkhäuser (2001) MR1792613
37 L Keen, C Series, Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori, Topology 32 (1993) 719 MR1241870
38 S P Kerckhoff, W P Thurston, Noncontinuity of the action of the modular group at Bers' boundary of Teichmüller space, Invent. Math. 100 (1990) 25 MR1037141
39 I Kim, C Lecuire, K Ohshika, Convergence of freely decomposable Kleinian groups arXiv:0708.3266
40 G Kleineidam, J Souto, Algebraic convergence of function groups, Comment. Math. Helv. 77 (2002) 244 MR1915041
41 S Kojima, Deformations of hyperbolic $3$–cone-manifolds, J. Differential Geom. 49 (1998) 469 MR1669649
42 I Kra, On spaces of Kleinian groups, Comment. Math. Helv. 47 (1972) 53 MR0306485
43 I Kra, Horocyclic coordinates for Riemann surfaces and moduli spaces. I: Teichmüller and Riemann spaces of Kleinian groups, J. Amer. Math. Soc. 3 (1990) 499 MR1049503
44 R S Kulkarni, P B Shalen, On Ahlfors' finiteness theorem, Adv. Math. 76 (1989) 155 MR1013665
45 P Lavaurs, Systèmes dynamiques holomorphes: Explosion de points périodique paraboliques, PhD thesis, Université Paris-Sud, Orsay (1989)
46 C Lecuire, An extension of the Masur domain, from: "Spaces of Kleinian groups", London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 49 MR2258744
47 A D Magid, Deformation spaces of Kleinian surface groups are not locally connected, PhD thesis, University of Michigan (2009)
48 A D Magid, Examples of relative deformation spaces that are not locally connected, Math. Ann. 344 (2009) 877 MR2507629
49 A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. 99 (1974) 383 MR0349992
50 A Marden, Outer circles: An introduction to hyperbolic $3$–manifolds, Cambridge Univ. Press (2007) MR2355387
51 B Maskit, Construction of Kleinian groups, from: "Proc. Conf. Complex Analysis (Minneapolis, 1964)" (editors A Aeppli, E Calabi, H Röhrl), Springer (1965) 281 MR0178138
52 B Maskit, On Klein's combination theorem, Trans. Amer. Math. Soc. 120 (1965) 499 MR0192047
53 B Maskit, On Klein's combination theorem. II, Trans. Amer. Math. Soc. 131 (1968) 32 MR0223570
54 B Maskit, Self-maps on Kleinian groups, Amer. J. Math. 93 (1971) 840 MR0291453
55 D McCullough, Compact submanifolds of $3$–manifolds with boundary, Quart. J. Math. Oxford Ser. 37 (1986) 299 MR854628
56 C T McMullen, The classification of conformal dynamical systems, from: "Current developments in mathematics, 1995 (Cambridge, MA)" (editors R Bott, M Hopkins, A Jaffe, I Singer, D Stroock, S T Yau), Int. Press (1994) 323 MR1474980
57 C T McMullen, Frontiers in complex dynamics, Bull. Amer. Math. Soc. 31 (1994) 155 MR1260523
58 C T McMullen, Renormalization and $3$–manifolds which fiber over the circle, Annals of Math. Studies 142, Princeton Univ. Press (1996) MR1401347
59 C T McMullen, Complex earthquakes and Teichmüller theory, J. Amer. Math. Soc. 11 (1998) 283 MR1478844
60 J Milnor, Remarks on iterated cubic maps, Experiment. Math. 1 (1992) 5 MR1181083
61 Y N Minsky, The classification of punctured-torus groups, Ann. of Math. 149 (1999) 559 MR1689341
62 J W Morgan, On Thurston's uniformization theorem for three-dimensional manifolds, from: "The Smith conjecture (New York, 1979)" (editors J W Morgan, H Bass), Pure Appl. Math. 112, Academic Press (1984) 37 MR758464
63 H Namazi, J Souto, Non-realizability and ending laminations, preprint (2010)
64 K Ohshika, Ending laminations and boundaries for deformation spaces of Kleinian groups, J. London Math. Soc. 42 (1990) 111 MR1078179
65 K Ohshika, Realising end invariants by limits of minimally parabolic, geometrically finite groups, Geom. Topol. 15 (2011) 827 MR2821565
66 J S Purcell, Cusp shapes under cone deformation, J. Differential Geom. 80 (2008) 453 MR2472480
67 G P Scott, Finitely generated $3$–manifold groups are finitely presented, J. London Math. Soc. 6 (1973) 437 MR0380763
68 D Sullivan, Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou–Julia problem on wandering domains, Ann. of Math. 122 (1985) 401 MR819553
69 D Sullivan, Quasiconformal homeomorphisms and dynamics II. Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985) 243 MR806415
70 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
71 W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
72 W P Thurston, Hyperbolic structures on $3$–manifolds I: Deformation of acylindrical manifolds, Ann. of Math. 124 (1986) 203 MR855294
73 F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. 87 (1968) 56 MR0224099
74 D J Wright, The shape of the boundary of Maskit's embedding of the Teichmüller space of once punctured tori, preprint (1987)