Finite covers of $3$-manifolds containing essential surfaces of Euler characteristic $=0$
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- by Sadayoshi Kojima PDF
- Proc. Amer. Math. Soc. 101 (1987), 743-747 Request permission
Abstract:
We give a short proof and a slight generalization of a theorem of John Luecke, that a compact connected orientable irreducible $3$-manifold containing an essential torus is finitely covered by a torus bundle or manifolds with unbounded first Betti numbers.References
- John Hempel, $3$-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619 —, Residual finiteness for $3$-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. J. Luecke, Finite covers of $3$-manifolds containing essential tori, preprint (1986).
- 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, DOI 10.1090/S0273-0979-1982-15003-0
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 743-747
- MSC: Primary 57N10; Secondary 57M10
- DOI: https://doi.org/10.1090/S0002-9939-1987-0911044-9
- MathSciNet review: 911044