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A hyperbolic-by-hyperbolic hyperbolic group
Author(s):
Lee
Mosher
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3447-3455.
MSC (1991):
Primary 20F32;
Secondary 57M07, 20F28
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Abstract:
Given a short exact sequence of finitely generated groups 
it is known that if  and  are word hyperbolic, and if  is nonelementary, then  is word hyperbolic. In the original examples due to Thurston, as well as later examples due to Bestvina and Feighn, the group  is elementary. We give a method for constructing examples where all three groups are nonelementary.
References:
- [BC88]
- S. Bleiler and A. Casson, Automorphisms of surfaces after Nielsen and Thurston, LMS Student Texts, vol. 9, Cambridge University Press, 1988. MR 89k:57025
- [BF92]
- M. Bestvina and M. Feighn, A combination theorem for negatively curved groups, J. Diff. Geom. 35 (1992), no. 1, 85-101. MR 93d:53053
- [BFH96]
- M. Bestvina, M. Feighn, and M. Handel, Laminations, trees, and irreducible automorphisms of free groups, Geometric and Functional Analysis (1997), to appear.
- [Bir74]
- J. Birman, Braids, links, and mapping class groups, Annals of Math. Studies, vol. 82, Princeton University Press, 1974. MR 51:11477
- [BLM83]
- J. Birman, A. Lubotsky, and J. McCarthy, Abelian and solvable subgroups of the mapping class group, Duke Math. J. 50 (1983), no. 4, 1107-1120. MR 85k:20126
- [Can91]
- J. Cannon, The theory of negatively curved spaces and groups, Ergodic theory, symbolic dynamics, and hyperbolic spaces (C. Series T. Bedford, M. Keane, ed.), Oxford Univ. Press, 1991. CMP 92:02
- [CT]
- J. Cannon and W. P. Thurston, Group invariant Peano curves, preprint.
- [FLP
 79] - A. Fathi, F. Laudenbach, V. Poenaru, et al., Travaux de Thurston sur les surfaces, Astérisque, vol. 66-67, Société Mathématique de France, Paris, 1979. MR 82m:57003
- [Mas94]
- H. Masur, 1994, private correspondence.
- [McC85]
- J. McCarthy, A ``Tits-alternative'' for subgroups of surface mapping class groups, Trans. AMS 291 (1985), no. 2, 583-612. MR 87f:57011
- [Mil68]
- J. Milnor, A note on curvature and fundamental group, J. Diff. Geom. 2 (1968), 1-7. MR 38:636
- [Mit]
- M. Mitra, Cannon-Thurston maps for hyperbolic group extensions, Topology (1997), to appear.
- [Mos96]
- L. Mosher, Hyperbolic extensions of groups, J. Pure and Appl. Alg. 110 (1996), no. 3, 305-314. MR 97c:20056
- [Ota96]
- J.-P. Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque, no. 235, Société mathématique de france, 1996. MR 97e:57013
- [RS95]
- E. Rips and Z. Sela, Cyclic splittings of finitely presented groups and the canonical JSJ decomposition, Annals of Math. (1997), to appear.
- [Sti87]
- J. Stillwell, The Dehn-Nielsen theorem, Papers on group theory and topology, by M. Dehn (J. Stillwell transl.), Springer, 1987.
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Additional Information:
Lee
Mosher
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102
Email:
mosher@andromeda.rutgers.edu
DOI:
10.1090/S0002-9939-97-04249-4
PII:
S 0002-9939(97)04249-4
Received by editor(s):
May 4, 1996
Additional Notes:
Partially supported by NSF grant # DMS-9204331
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1997,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Bestvina, M.; Feighn, M.; Handel, M., Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997), 215--244. MR 98c:20045
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