Hyperbolic groups with low-dimensional boundary

Kapovich, Michael; Kleiner, Bruce

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 5, pp. 647-669.

[1] Alonso J.M., Brady T., Cooper D., Delzant T., Ferlini V., Lustig M., Mihalik M., Shapiro M., Short H., Notes on negatively curved groups, Preprint, 1989.

[2] Anderson R.D., A characterization of the universal curve and a proof of its homogeneity, Ann. Math. 67 (1958) 313-324. | MR | Zbl

[3] Anderson R.D., One-dimensional continuous curves and a homogeneity theorem, Ann. Math. 68 (1958) 1-16. | MR | Zbl

[4] Andreev E., On convex polyhedra in Lobachevsky space, Math. USSR Sbornik 10 (1970) 413-440. | Zbl

[5] Benakli N., Groupes hyperboliques de bord la courbe de Menger ou la courbe de Sierpinski, Preprint, Paris, 1991.

[6] Bestvina M., Characterizing k-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 71 (380) (1988). | MR | Zbl

[7] Bestvina M., Local homology properties of boundaries of groups, Mich. Math. J. 43 (1) (1996) 123-139. | MR | Zbl

[8] Bestvina M., Feighn M., Bounding the complexity of group actions on trees, Invent. Math. 103 (1991) 449-469. | MR | Zbl

[9] Bestvina M., Feighn M., A combination theorem for hyperbolic groups, J. Differential Geom. 35 (1992) 85-101. | MR | Zbl

[10] Bestvina M., Feighn M., Addendum and correction to : “A combination theorem for negatively curved groups”, J. Differential Geom. 43 (1996) 783-788. | MR | Zbl

[11] Bestvina M., Mess G., The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991) 469-481. | MR | Zbl

[12] Bowditch B.H., Notes on Gromov's hyperbolicity criterion for path-metric spaces, in : Ghys E., Haefliger A., Verjovsky A. (Eds.), Group Theory from a Geometrical Point of View (ICTP, Trieste, April 1990), 1991, pp. 64-167. | MR | Zbl

[13] Bowditch B.H., Connectedness properties of limit sets, Trans. Amer. Math. Soc. 351 (1999) 3673-3686. | MR | Zbl

[14] Bowditch B.H., A topological characterization of hyperbolic groups, J. Amer. Math. Soc. 11 (3) (1998) 643-667. | MR | Zbl

[15] Bowditch B.H., Convergence groups and configuration spaces, in : Proceedings of the Camberra Group Theory Conference, 1996 (to appear). | Zbl

[16] Casson A., Bleiler S., Automorphisms of Surfaces After Nielsen and Thurston, Cambridge Univ. Press, 1983. | Zbl

[17] Casson A., Jungreis D., Convergence groups and Seifert fibered 3-manifolds, Invent. Math. 118 (F. 3) (1994) 441-456. | MR | Zbl

[18] Champetier C., Propriétés statistiques des groupes de presentation finie, Adv. Math. 116 (1995) 197-262. | MR | Zbl

[19] Claytor S., Topological immersion of Peanian continua in the spherical surface, Ann. Math. 35 (1924) 809-835. | JFM | Zbl

[20] Davis M., Januszkiewicz T., Hyperbolization of polyhedra, J. Differential Geom. 34 (1991) 347-388. | MR | Zbl

[21] Dranishnikov A., (private communication).

[22] Dicks W., Dunwoody M., Groups Acting on Graphs, Cambridge Studies in Advanced Mathematics, Vol. 17, 1989. | MR | Zbl

[23] Eberlein P., O'Neill B., Visibility manifolds, Pacific J. Math. 46 (1973) 45-109. | MR | Zbl

[24] Gabai D., Convergence groups are Fuchsian groups, Ann. Math. 136 (1992) 447-510. | MR | Zbl

[25] Ghys E., De La Harpe P., Sur les Groupes Hyperbolic d'Apres Mikhael Gromov, Progress in Mathematics, Vol. 83, Birkhäuser, 1990. | Zbl

[26] Gromov M., Hyperbolic groups, in : Essays in Group Theory, Publications of MSRI, Vol. 8, 1987, pp. 75-264. | MR | Zbl

[27] Hempel J., Residual finiteness for 3-manifolds, in : Combinatorial Group Theory and Topology (Alta, Utah, 1984), Annals of Math. Studies, Vol. 111, Princeton Univ. Press, 1987, pp. 379-396. | MR | Zbl

[28] Jaco W., Shalen P., Seifert fibred spaces in 3-manifolds, Mem. Amer. Math. Soc. 220 (1979). | Zbl

[29] Johannson K., Homotopy-equivalences of 3-Manifolds with Boundary, Lect. Notes in Math., Vol. 761, Springer-Verlag, 1979. | MR | Zbl

[30] Kapovich M., Deformations of representations of discrete subgroups of SO(3,1), Math. Ann. 299 (1994) 341-354. | MR | Zbl

[31] Kapovich M., Kleiner B., Coarse Alexander duality and duality groups, Preprint, 1999.

[32] Kleiner B., Leeb B., Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Math. Publ. of Inst. Hautes Études Sci. 86 (1997) 115-197. | Numdam | MR | Zbl

[33] Mitra M., Height in splittings of hyperbolic groups, Preprint, 1997.

[34] Moise E.E., Remarks on the Claytor embedding theorem, Duke Math. J. 19 (1952) 199-202. | MR | Zbl

[35] Pansu P., Métriques de Carnot-Carathéodory et quasi-isométries des espaces symétriques de rang un, Ann. Math. 129 (1989) 1-60. | MR | Zbl

[36] Rips E., Subgroups of small cancellation groups, Bull. London Math. Soc. 14 (1982) 45-47. | MR | Zbl

[37] Schwartz R., The quasi-isometry classification of rank one lattices, Math. Publ. of Inst. Hautes Études Sci. 82 (1995) 133-168. | Numdam | MR | Zbl

[38] Scott P., The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983) 401-487. | MR | Zbl

[39] Scott P., Wall T., Topological methods in group theory, in : Homological Group Theory, London Math. Soc. Lecture Notes, Vol. 36, 1979, pp. 137-204. | MR | Zbl

[40] Stallings J., On torsion-free groups with infinitely many ends, Ann. Math. 88 (1968) 312-334. | MR | Zbl

[41] Swarup G.A., On the cut-point conjecture, Electronic Research Announcements of Amer. Math. Soc. 2 (1996) 98-100. | MR | Zbl

[42] Swarup G.A., Proof of a weak hyperbolization theorem, Preprint, 1998.

[43] Tukia P., Homeomorphic conjugates of fuchsian groups, J. Reine Angew. Math. 391 (1988) 1-54. | MR | Zbl

[44] Tukia P., Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (2) (1994) 157-187. | MR | Zbl

[45] Whyburn G.T., Topological characterization of the Sierpinski curve, Fundamenta Math. 45 (1958) 320-324. | MR | Zbl