Geometry & Topology Volume 9, issue 1 (2005)

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Kleinian groups and the rank problem

Ilya Kapovich and Richard Weidmann

Geometry & Topology 9 (2005) 375–402

DOI: 10.2140/gt.2005.9.375

Bibliography

1	I Agol, Tameness of hyperbolic 3–manifolds arXiv:math.GT/0405568
2	J M Alonso, e al., Notes on word hyperbolic groups, from: "Group theory from a geometrical viewpoint (Trieste, 1990)", World Sci. Publ., River Edge, NJ (1991) 3 MR1170363
3	G N Arzhantseva, On quasiconvex subgroups of word hyperbolic groups, Geom. Dedicata 87 (2001) 191 MR1866849
4	G N Arzhantseva, A Y Ol’shanskiĭ, Generality of the class of groups in which subgroups with a lesser number of generators are free, Mat. Zametki 59 (1996) 489, 638 MR1445193
5	G Baumslag, C F Miller III, H Short, Unsolvable problems about small cancellation and word hyperbolic groups, Bull. London Math. Soc. 26 (1994) 97 MR1246477
6	M Boileau, H Zieschang, Heegaard genus of closed orientable Seifert 3–manifolds, Invent. Math. 76 (1984) 455 MR746538
7	D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3–manifolds, J. Amer. Math. Soc. 19 (2006) 385 MR2188131
8	R D Canary, A covering theorem for hyperbolic 3–manifolds and its applications, Topology 35 (1996) 751 MR1396777
9	N M Dunfield, W P Thurston, The virtual Haken conjecture: experiments and examples, Geom. Topol. 7 (2003) 399 MR1988291
10	D B A Epstein, J W Cannon, D F Holt, S V F Levy, M S Paterson, W P Thurston, Word processing in groups, Jones and Bartlett Publishers (1992) MR1161694
11	D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. $(2)$ 136 (1992) 447 MR1189862
12	, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics 83, Birkhäuser (1990) MR1086648
13	V Gerasimov, Detecting connectedness of the boundary of a hyperbolic group, preprint (1999)
14	S M Gersten, H B Short, Rational subgroups of biautomatic groups, Ann. of Math. $(2)$ 134 (1991) 125 MR1114609
15	M Gromov, Hyperbolic groups, from: "Essays in group theory", Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
16	W Jaco, J H Rubinstein, 0–efficient triangulations of 3–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
17	K Johannson, Topology and combinatorics of 3–manifolds, Lecture Notes in Mathematics 1599, Springer (1995) MR1439249
18	I Kapovich, Detecting quasiconvexity: algorithmic aspects, from: "Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994)", DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer. Math. Soc. (1996) 91 MR1364182
19	I Kapovich, R Weidmann, A Miasnikov, Foldings, graphs of groups and the membership problem, Internat. J. Algebra Comput. 15 (2005) 95 MR2130178
20	I Kapovich, H Short, Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups, Canad. J. Math. 48 (1996) 1224 MR1426902
21	I Kapovich, R Weidmann, Nielsen methods and groups acting on hyperbolic spaces, Geom. Dedicata 98 (2003) 95 MR1988426
22	I Kapovich, R Weidmann, Freely indecomposable groups acting on hyperbolic spaces, Internat. J. Algebra Comput. 14 (2004) 115 MR2058318
23	M Kapovich, Hyperbolic manifolds and discrete groups, Progress in Mathematics 183, Birkhäuser (2001) MR1792613
24	W Magnus, A Karrass, D Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers, New York-London-Sydney (1966) MR0207802
25	P Papasoglu, An algorithm detecting hyperbolicity, from: "Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994)", DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Amer. Math. Soc. (1996) 193 MR1364185
26	E Rips, Subgroups of small cancellation groups, Bull. London Math. Soc. 14 (1982) 45 MR642423
27	J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
28	P E Schupp, Coxeter groups, 2–completion, perimeter reduction and subgroup separability, Geom. Dedicata 96 (2003) 179 MR1956839
29	Z Sela, The isomorphism problem for hyperbolic groups I, Ann. of Math. $(2)$ 141 (1995) 217 MR1324134
30	C C Sims, Computation with finitely presented groups, Encyclopedia of Mathematics and its Applications 48, Cambridge University Press (1994) MR1267733
31	J Souto, The rank of the fundamental group of hyperbolic 3–manifolds fibering over the circle, preprint (2005)
32	P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1 MR961162
33	R Weidmann, The Nielsen method for groups acting on trees, Proc. London Math. Soc. $(3)$ 85 (2002) 93 MR1901370
34	R Weidmann, The rank problem for sufficiently large Fuchsian groups, Proc. Lond. Math. Soc. $(3)$ 95 (2007) 609 MR2368278