### Impacto

Montesinos Amilibia, José María
(1987)
*On 3-manifolds having surface bundles as branched coverings.*
Proceedings of the American Mathematical Society, 101
(3).
pp. 555-558.
ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1987-101-03/S0002-9939-1987-0908668-1/S0002-9939-1987-0908668-1.pdf

## Abstract

We give a different proof of the result of M. Sakuma [Math. Sem. Notes Kobe Univ. 9 (1981), no. 1, 159–180] that every closed, oriented 3-manifold M has a 2-fold branched covering space N which is a surface bundle over S1. 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 S3 for a number of different m's as big as we like.

Item Type: | Article |
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Uncontrolled Keywords: | open-book; hyperbolic manifold; surface bundle over S 1 ; closed orientable 3-manifold; 2m-fold branched cyclic covering |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 17155 |

References: | R. Brooks, On branched coverings of 3-manifolds which fiber over the circle, J. Reine Angew. Math. 362 (1985), 87-101. A. Casson and C. Gordon, Talk by Casson, Workshop of Low Dimensional Topology, Berkeley, 1985. A. Fathi, Dehn twists and pseudo-Anosov diffeomorphisms (preprint). F. González-Acuña, 3-dimensional open books, Lectures, Univ. of Iowa, Topological Seminar, 1974/75. U. Hirsch and W. Neumann, On cyclic branched coverings of spheres, Math. Ann. 215 (1975), 289-291. J. Montesinos, Surgery on links and double branched covers of S3, Knots, Groups and 3-Manifolds (L. P. Neuwirth, ed.), Ann. of Math. Studies, no. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 227-259. R. Myers, Open book decompositions of 3-manifolds, Proc. Amer. Math. Soc. 72 (1978), 397-402. M. Sakuma, Surface bundles over S1 which are 2-fold branched cyclic coverings of S3, Math. Sem. Notes 9 (1981), 159-180. T. Soma, Hyperbolic, fibred links and fibre-concordances, Math. Proc. Cambridge Philos. Soc. 96 (1984), 283-294. J. R. Stallings, Constructions of fibred knots and links, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R.I., 1978, pp. 55-60. |

Deposited On: | 20 Nov 2012 12:55 |

Last Modified: | 07 Feb 2014 09:42 |

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