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Epimorphism sequences between hyperbolic 3-manifold groups
Author:
Teruhiko Soma
Journal:
Proc. Amer. Math. Soc. 130 (2002), 1221-1223
MSC (1991):
Primary 57M50, 57M05
Posted:
August 29, 2001
MathSciNet review:
1873800
Full-text PDF Free Access
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Additional Information
Abstract: We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.
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1669645 (2000b:57034)
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Soma, Sequences of degree-one maps between geometric
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733–742. MR 1758451
(2001b:57039), http://dx.doi.org/10.1007/s002080050352
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S. Wang and Q. Zhou, Any
 -manifold  -dominates at most finitely many geometric  -manifolds, E-print: math.GT/0001058.
- 1.
- D. Cooper, M. Culler, H. Gillet, D.D. Long and P.B. Shalen, Plane curves associated to character varieties of
 -manifolds, Invent. Math. 118 (1994), 47-84. MR 95g:57029
- 2.
- M. Culler and P.B. Shalen, Varieties of group representations and splitting of
 -manifolds, Ann. of Math. 117 (1983), 109-146. MR 84k:57005
- 3.
- R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics vol 52, Springer-Verlag, New York Heiderberg Berlin, 1977. MR 57:3116
- 4.
- C. Hayat-Legrand, S. Wang and H. Zieschang, Any -manifold -dominates at most finitely many Seifert manifolds with finite fundamental groups, Peking University Research Report No. 82, (1999), preprint.
- 5.
- R. Kirby, Problems in low-dimensional topology, Geometric Topology (W.H. Kazez ed.), AMS/IP Studies in Advanced Mathematics vol. 2, Part 2, Amer. Math. Soc. and International Press, 1997, pp. 35-473. CMP 98:01
- 6.
- A.W. Reid and S. Wang, Non-Haken
 -manifolds are not large with respect to mappings of non-zero degree, Comm. Anal. Geom. 7 (1999), 105-132. MR 2000c:57042
- 7.
- A.W. Reid, S. Wang and Q. Zhou, Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for -manifold groups, E-print: math.GT/0002003.
- 8.
- Y. Rong, Degree one maps between geometric
 -manifolds, Trans. Amer. Math. Soc. 332 (1992), 411-436. MR 92j:57007
- 9.
- T. Soma, Non-zero degree maps to hyperbolic
 -manifolds, J. Differential Geom. 49 (1998), 517-546. MR 2000b:57034
- 10.
- T. Soma, Sequences of degree-one maps between geometric
 -manifolds, Math. Ann. 316 (2000), 733-742. MR 2001b:57039
- 11.
- S. Wang and Q. Zhou, Any -manifold -dominates at most finitely many geometric -manifolds, E-print: math.GT/0001058.
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Additional Information
Teruhiko Soma
Affiliation:
Department of Mathematical Sciences, School of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama-ken 350-0394, Japan
Email:
soma@r.dendai.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-01-06126-3
PII:
S 0002-9939(01)06126-3
Keywords:
Hyperbolic $3$-manifolds,
character varieties
Received by editor(s):
July 11, 2000
Received by editor(s) in revised form:
September 27, 2000
Posted:
August 29, 2001
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 2001 American Mathematical Society
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