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Finite covers of  -manifolds containing essential surfaces of Euler characteristic 
Author:
Sadayoshi Kojima
Journal:
Proc. Amer. Math. Soc. 101 (1987), 743-747
MSC:
Primary 57N10; Secondary 57M10
MathSciNet review:
911044
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Abstract: We give a short proof and a slight generalization of a theorem of John Luecke, that a compact connected orientable irreducible  -manifold containing an essential torus is finitely covered by a torus bundle or manifolds with unbounded first Betti numbers.
- [1]
John
Hempel, 3-Manifolds, Princeton University Press, Princeton, N.
J., 1976. Ann. of Math. Studies, No. 86. MR 0415619
(54 #3702)
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-, Residual finiteness for
 -manifolds, Combinatorial Group Theory and Topology, edited by S. Gersten and J. Stallings, Ann. of Math. Studies, no. 111, Princeton Univ. Press, Princeton, N. J., 1987, pp. 379-396.
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J. Luecke, Finite covers of
 -manifolds containing essential tori, preprint (1986).
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William
P. Thurston, Three-dimensional manifolds, Kleinian
groups and hyperbolic geometry, Bull. Amer.
Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524
(83h:57019), http://dx.doi.org/10.1090/S0273-0979-1982-15003-0
- [1]
- J. Hempel,
 -manifolds, Ann. of Math. Studies, no. 86, Princeton Univ. Press, Princeton, N.J., 1976. MR 0415619 (54:3702)
- [2]
- -, Residual finiteness for -manifolds, Combinatorial Group Theory and Topology, edited by S. Gersten and J. Stallings, Ann. of Math. Studies, no. 111, Princeton Univ. Press, Princeton, N. J., 1987, pp. 379-396.
- [3]
- J. Luecke, Finite covers of -manifolds containing essential tori, preprint (1986).
- [4]
- W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), 357-381. MR 648524 (83h:57019)
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DOI:
http://dx.doi.org/10.1090/S0002-9939-1987-0911044-9
PII:
S 0002-9939(1987)0911044-9
Keywords:
 -manifold,
essential surface,
residual finiteness
Article copyright:
© Copyright 1987 American Mathematical Society
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