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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Finite covers of $ 3$-manifolds containing essential tori


Author: John Luecke
Journal: Trans. Amer. Math. Soc. 310 (1988), 381-391
MSC: Primary 57N10; Secondary 57M10
MathSciNet review: 965759
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Abstract: It is shown in this paper that if a Haken $ 3$-manifold contains an incompressible torus that is not boundary-parallel then either it has a finite cover that is a torus-bundle over the circle or it has finite covers with arbitrarily large first Betti number.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0965759-2
PII: S 0002-9947(1988)0965759-2
Article copyright: © Copyright 1988 American Mathematical Society