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On $ 3$-manifolds having surface bundles as branched coverings


Author: José María Montesinos
Journal: Proc. Amer. Math. Soc. 101 (1987), 555-558
MSC: Primary 57M12; Secondary 57M25, 57N10
DOI: https://doi.org/10.1090/S0002-9939-1987-0908668-1
MathSciNet review: 908668
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Abstract: We give a different proof of the result of Sakuma that every closed, oriented $ 3$-manifold $ M$ has a $ 2$-fold branched covering space $ N$ which is a surface bundle over $ {S^1}$. We also give a new proof of the result of Brooks that $ N$ can be made hyperbolic. We give examples of irreducible $ 3$-manifolds which can be represented as $ 2m$-fold cyclic branched coverings of $ {S^3}$ for a number of different $ m$'s as big as we like.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0908668-1
Keywords: Branched covering, surface-bundle, fibered knot, hyperbolic knot, hyperbolic manifold, open-book, cyclic covering
Article copyright: © Copyright 1987 American Mathematical Society

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