Volume 16, issue 3 (2012)

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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
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)