Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finite covers of $ 3$-manifolds containing essential surfaces of Euler characteristic $ =0$


Author: Sadayoshi Kojima
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. Hempel, $ 3$-manifolds, Ann. of Math. Studies, no. 86, Princeton Univ. Press, Princeton, N.J., 1976. MR 0415619 (54:3702)
  • [2] -, 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.
  • [3] J. Luecke, Finite covers of $ 3$-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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 57M10

Retrieve articles in all journals with MSC: 57N10, 57M10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0911044-9
Keywords: $ 3$-manifold, essential surface, residual finiteness
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society