Volume 15, issue 2 (2011)

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

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Realising end invariants by limits of minimally parabolic, geometrically finite groups

Ken’ichi Ohshika

Geometry & Topology 15 (2011) 827–890
Bibliography
1 W Abikoff, On boundaries of Teichmüller spaces and on Kleinian groups. III, Acta Math. 134 (1975) 211 MR0435452
2 I Agol, Tameness of hyperbolic $3$–manifolds arXiv:math/0405568
3 L Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. $(2)$ 91 (1970) 570 MR0297992
4 L Bers, An inequality for Riemann surfaces, from: "Differential geometry and complex analysis" (editors I Chavel, H M Farkas), Springer (1985) 87 MR780038
5 M Bestvina, Degenerations of the hyperbolic space, Duke Math. J. 56 (1988) 143 MR932860
6 F Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. $(4)$ 16 (1983) 237 MR732345
7 F Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. $(2)$ 124 (1986) 71 MR847953
8 F Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988) 139 MR931208
9 J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33 MR2079598
10 J F Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups, II: The Ending Lamination Conjecture arXiv:math.GT/0412006
11 J F Brock, J Souto, Algebraic limits of geometrically finite manifolds are tame, Geom. Funct. Anal. 16 (2006) 1 MR2221251
12 K W Bromberg, Projective structures with degenerate holonomy and the Bers density conjecture, Ann. of Math. $(2)$ 166 (2007) 77 MR2342691
13 R Brooks, J P Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982) 163 MR650375
14 D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
15 R D Canary, The Poincaré metric and a conformal version of a theorem of Thurston, Duke Math. J. 64 (1991) 349 MR1136380
16 R D Canary, Ends of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 6 (1993) 1 MR1166330
17 R D Canary, A covering theorem for hyperbolic $3$–manifolds and its applications, Topology 35 (1996) 751 MR1396777
18 R D Canary, The conformal boundary and the boundary of the convex core, Duke Math. J. 106 (2001) 193 MR1810370
19 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
20 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, 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) 113 MR903852
21 A Fathi, F Laudenbach, V Poenaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66–67, Soc. Math. France (1979) 284 MR568308
22 M Freedman, J Hass, P Scott, Least area incompressible surfaces in $3$–manifolds, Invent. Math. 71 (1983) 609 MR695910
23 D Gabai, The simple loop conjecture, J. Differential Geom. 21 (1985) 143 MR806708
24 W H Jaco, P B Shalen, Seifert fibered spaces in $3$–manifolds, Mem. Amer. Math. Soc. 21 (1979) MR539411
25 K Johannson, Homotopy equivalences of $3$–manifolds with boundaries, Lecture Notes in Math. 761, Springer (1979) MR551744
26 I Kim, C Lecuire, K Ohshika, Convergence of freely decomposable Kleinian groups arXiv:0708.3266
27 G Kleineidam, J Souto, Algebraic convergence of function groups, Comment. Math. Helv. 77 (2002) 244 MR1915041
28 C Lecuire, An extension of the Masur domain, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 49 MR2258744
29 C Lecuire, Plissage des variétés hyperboliques de dimension 3, Invent. Math. 164 (2006) 85 MR2207784
30 B Maskit, Parabolic elements in Kleinian groups, Ann. of Math. $(2)$ 117 (1983) 659 MR701259
31 H A Masur, Y N Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
32 H A Masur, Y N Minsky, Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902 MR1791145
33 D McCullough, Compact submanifolds of $3$–manifolds with boundary, Quart. J. Math. Oxford Ser. $(2)$ 37 (1986) 299 MR854628
34 Y N Minsky, Teichmüller geodesics and ends of hyperbolic $3$–manifolds, Topology 32 (1993) 625 MR1231968
35 Y N Minsky, On rigidity, limit sets, and end invariants of hyperbolic $3$–manifolds, J. Amer. Math. Soc. 7 (1994) 539 MR1257060
36 Y N Minsky, The classification of punctured-torus groups, Ann. of Math. $(2)$ 149 (1999) 559 MR1689341
37 Y N Minsky, Kleinian groups and the complex of curves, Geom. Topol. 4 (2000) 117 MR2182094
38 Y N Minsky, The classification of Kleinian surface groups. I. Models and bounds, Ann. of Math. (2) 171 (2010) 1 MR2630036
39 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
40 J W Morgan, J P Otal, Relative growth rates of closed geodesics on a surface under varying hyperbolic structures, Comment. Math. Helv. 68 (1993) 171 MR1214228
41 J W Morgan, P B Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. $(2)$ 120 (1984) 401 MR769158
42 J W Morgan, P B Shalen, Degenerations of hyperbolic structures. II. Measured laminations in $3$–manifolds, Ann. of Math. $(2)$ 127 (1988) 403 MR932305
43 H Namazi, J Souto, Non-realizability, ending laminations and the density conjecture, preprint (2010)
44 K Ohshika, Ending laminations and boundaries for deformation spaces of Kleinian groups, J. London Math. Soc. $(2)$ 42 (1990) 111 MR1078179
45 K Ohshika, Limits of geometrically tame Kleinian groups, Invent. Math. 99 (1990) 185 MR1029395
46 K Ohshika, Geometric behaviour of Kleinian groups on boundaries for deformation spaces, Quart. J. Math. Oxford Ser. $(2)$ 43 (1992) 97 MR1150472
47 K Ohshika, Geometrically finite Kleinian groups and parabolic elements, Proc. Edinburgh Math. Soc. $(2)$ 41 (1998) 141 MR1604337
48 K Ohshika, Rigidity and topological conjugates of topologically tame Kleinian groups, Trans. Amer. Math. Soc. 350 (1998) 3989 MR1451613
49 K Ohshika, Kleinian groups which are limits of geometrically finite groups, Mem. Amer. Math. Soc. 177 (2005) MR2154090
50 K Ohshika, Constructing geometrically infinite groups on boundaries of deformation spaces, J. Math. Soc. Japan 61 (2009) 1261 MR2588511
51 K Ohshika, H Miyachi, On topologically tame Kleinian groups with bounded geometry, from: "Spaces of Kleinian groups" (editors Y N Minsky, M Sakuma, C Series), London Math. Soc. Lecture Note Ser. 329, Cambridge Univ. Press (2006) 29 MR2258743
52 J P Otal, Courants géodésiques et produits libres, Thèse d’Etat, Université Paris-Sud, Orsay (1988)
53 J P Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235, Soc. Math. France (1996) MR1402300
54 F Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1988) 53 MR958589
55 G P Scott, Compact submanifolds of $3$–manifolds, J. London Math. Soc. $(2)$ 7 (1973) 246 MR0326737
56 R K Skora, Splittings of surfaces, J. Amer. Math. Soc. 9 (1996) 605 MR1339846
57 T Sugawa, Uniform perfectness of the limit sets of Kleinian groups, Trans. Amer. Math. Soc. 353 (2001) 3603 MR1837250
58 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
59 F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56 MR0224099