Self-embeddings of Kleinian groups

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 31, Issue 3, 1998, Pages 329-343

  Ohshika, Ken'ichi ^a   Potyagailo, Leonid ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032061984     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(98)80137-7     Document Type: Article

References (31)

1. [B] R. BAER, Groups without proper isomorphic quotient groups, (Bull. Amer. Math. Soc., Vol. 50, 1944, pp. 267-278).
2. [Bo] F. BONAHON, Cobordism of automorphisms of surfaces, (Ann. Sci. Ecole Norm. Sup., Vol. 16 (4), 1983, pp. 237-270).
3. [Be] M. BESTVINA, Degenerations of the hyperbolic space, (Duke Math. J., Vol. 56, 1988, pp. 143-161).
4. [Be-F] M. BESTVINA and M. FEIGHN, Stable actions of groups on real trees, (Inv. Math., Vol. 121, 1995, pp. 287-321).
5. [Ca] R. CANARY, A covering theorem for hyperbolic 3-manifold and its applications, (Topology, Vol. 35, 1996, pp. 751-778).
6. [CEG] R. D. CANARY, D. B. A. EPSTEIN, P. Green, Notes on notes of Thurston, Analytical and geometric aspects of hyperbolic spaces 3-92 (London Math. Soc. Lecture Note Ser. Vol. 111 Cambridge Univ. Press 1987).
7. [De] T. DELZANT, L'image d'un groupe dans un groupe hyperbolique, (Comment. Math. Hetvetici Vol. 70, 1995, pp. 267-284).
8. [GW] F. GONZALES-ACUNA and W. WHITTEN, Embeddings of 3-manifold groups, (Mem. Amer. Math. Soc., No 474).
9. [GLW] F. GONZALES-ACUNA, R. LITHERLAND and W. WHITTEN, Cohopficity of Seifert bundle groups, (Trans. Amer. Math. Society, Vol. 341, 1994, No 1, pp. 143-155).
10. [Gro] M. GROMOV, Hyperbolic groups, in Essays in Group Theory, Ed. : S.M. Gersten, M.S.R.I. Pub. 8, Springer Verlag 1987.
11. [H] M. HEINS, On a problem of H. Hopf, (Jour. de. Math., Vol. 37, 1958, pp. 153-160).
12. [He] J. HEMPEL, 3-manifolds, (Ann. Math. Studies, 86, Princeton Univ).
13. [Ka] M. KAPOVICH, Notes on Thurston hyperbolization theorem, Preprint, University of Utah, 1997 (book in preparation).
14. [JMP] T. JORGENSEN, A. MARDEN, C. POMMERENKE, Two examples of covering surfaces, In: Riemann Surfaces and Related Topics, I. KRA and B. MASKIT ed., pp 305-319, (Ann. Math. Studies, 97, Princeton, 1978).
15. [Mar] A. MARDEN, The geometry of finitely generated Kleinian groups, (Ann. Math., Vol. 99, 1974, pp. 383-462).
16. [Ma] B. MASKIT, Kleinian groups, Springer Verlag, 1987.
17. [Mc] D. MCCULLOUGH, Compact submanifolds of 3-manifolds with boundary, (Quart. J. Math. Oxford Vol. 37, 1986, pp. 299-307).
18. [MMS] D. MCCULLOUGH, A. MILLER and G. A. SWARUP, Uniqueness of cores of non-compact 3-manifolds, (J. London Math. Soc., Vol. 32, 1985, pp. 548-556).
19. [Mo1] J. W. MORGAN, On Thurston's uniformization theorem for three-dimensional manifolds, in "The Smith Conjecture", edited by H. BASS and J. W. MORGAN, (Academic Press, 1984, pp. 37-125).
20. [Mo2] J.W. MORGAN, Croup actions on trees and compactifications of the space of classes of SO(n,1)-representations, (Topology, Vol. 25, 1986, pp. 1-33).
21. [MS] J.W. MORGAN and P. SHALEN, Valuations, trees and degeneration of hyperbolic structures, (Ann. of Math., Vol. 122, 1985, pp. 398-476).
22. [O1] J.P. OTAL, Le théorème d'hyperbolisation pour les varétés fibrées de dimension 3, (Astérisque, No 235, 1996, 206 p).
23. [Pa] F. PAULIN, Outer automorphisms of hyperbolic groups and small actions on R-trees, In: "Arboreal group theory", R. ALPERIN ed., pp. 331-343, (Pub M.S.R.I., 19, Springer-Verlag 1991).
24. [PW] L. POTYAGAILO and S. WANG, On the cohopficity of 3-manifold and Kleinian groups, preprint (IHES, 1992).
25. [RS] E. RIPS and Z. SELA, Structure and rigidity in hyperbolic groups I, (Geom. and Func. Anal., Vol. 4, 1994, pp. 337-371).
26. [Sc] G. P. SCOTT, Compact submanifolds of 3-manifolds, (J. London Math. Soc., Vol. 7, 1973, pp. 246-250).
27. [Se] Z. SELA, Structure, and Rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie group, II. (Geom. and Func. Anal., Vol. 7, 1997, pp. 561-593).
28. [Th1] W. THURSTON, Geometry and topology on 3-manifolds, Preprint Princeton, 1978.
29. [Th2] W. THURSTON, Hyperbolic structures on 3-manifolds I: Deformation of acylindrical manifolds, (Ann. of Math., Vol. 124, 1986, pp. 203-246).
30. [WW] S. WANG and Y. WU, A covering invariant of graph manifolds, (Proc. London Math. Soc., Vol. 68 (3), 1994, pp. 203-224).
31. [WZ] S. WANG S. and Q. ZHOU, On the proper conjugation of Kleinian groups, (Geom. Dedicata, Vol. 56, No 2, 1995, pp. 145-154).