Epimorphism sequences between hyperbolic 3-manifold groups
HTML articles powered by AMS MathViewer
- by Teruhiko Soma
- Proc. Amer. Math. Soc. 130 (2002), 1221-1223
- DOI: https://doi.org/10.1090/S0002-9939-01-06126-3
- Published electronically: August 29, 2001
- PDF | Request permission
Abstract:
We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.References
- D. Cooper, M. Culler, H. Gillet, D. D. Long, and P. B. Shalen, Plane curves associated to character varieties of $3$-manifolds, Invent. Math. 118 (1994), no. 1, 47–84. MR 1288467, DOI 10.1007/BF01231526
- Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, DOI 10.2307/2006973
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157, DOI 10.1007/978-1-4757-3849-0
- C. Hayat-Legrand, S. Wang and H. Zieschang, Any $3$-manifold $1$-dominates at most finitely many Seifert manifolds with finite fundamental groups, Peking University Research Report No. 82, (1999), preprint.
- 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.
- Alan W. Reid and Shicheng Wang, Non-Haken $3$-manifolds are not large with respect to mappings of non-zero degree, Comm. Anal. Geom. 7 (1999), no. 1, 105–132. MR 1674109, DOI 10.4310/CAG.1999.v7.n1.a4
- A.W. Reid, S. Wang and Q. Zhou, Generalized Hopfian property, minimal Haken manifold, and J. Simon’s conjecture for $3$-manifold groups, E-print: arXiv:math.GT/0002003.
- Yong Wu Rong, Degree one maps between geometric $3$-manifolds, Trans. Amer. Math. Soc. 332 (1992), no. 1, 411–436. MR 1052909, DOI 10.1090/S0002-9947-1992-1052909-6
- Teruhiko Soma, Non-zero degree maps to hyperbolic $3$-manifolds, J. Differential Geom. 49 (1998), no. 3, 517–546. MR 1669645
- Teruhiko Soma, Sequences of degree-one maps between geometric 3-manifolds, Math. Ann. 316 (2000), no. 4, 733–742. MR 1758451, DOI 10.1007/s002080050352
- S. Wang and Q. Zhou, Any $3$-manifold $1$-dominates at most finitely many geometric $3$-manifolds, E-print: arXiv:math.GT/0001058.
Bibliographic Information
- Teruhiko Soma
- Affiliation: Department of Mathematical Sciences, School of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama-ken 350-0394, Japan
- MR Author ID: 192547
- Email: soma@r.dendai.ac.jp
- Received by editor(s): July 11, 2000
- Received by editor(s) in revised form: September 27, 2000
- Published electronically: August 29, 2001
- Communicated by: Ronald A. Fintushel
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1221-1223
- MSC (1991): Primary 57M50, 57M05
- DOI: https://doi.org/10.1090/S0002-9939-01-06126-3
- MathSciNet review: 1873800