Epimorphism sequences between hyperbolic 3-manifold groups

Author:
Teruhiko Soma

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

Published electronically:
August 29, 2001

MathSciNet review:
1873800

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We will show that any infinite sequence of epimorphisms between finitely generated hyperbolic 3-manifold groups eventually consists of isomorphisms.

**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:
https://doi.org/10.1090/S0002-9939-01-06126-3

Keywords:
Hyperbolic $3$-manifolds,
character varieties

Received by editor(s):
July 11, 2000

Received by editor(s) in revised form:
September 27, 2000

Published electronically:
August 29, 2001

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 2001
American Mathematical Society