On 3-manifolds having surface bundles as branched coverings

Montesinos, José María

doi:10.1090/S0002-9939-1987-0908668-1

On $3$-manifolds having surface bundles as branched coverings
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Proc. Amer. Math. Soc. 101 (1987), 555-558 Request permission

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.

References

Robert Brooks, On branched coverings of $3$-manifolds which fiber over the circle, J. Reine Angew. Math. 362 (1985), 87–101. MR 809968, DOI 10.1515/crll.1985.362.87

Talk by Casson

Albert Fathi, Dehn twists and pseudo-Anosov diffeomorphisms, Invent. Math. 87 (1987), no. 1, 129–151. MR 862715, DOI 10.1007/BF01389156

-dimensional open books

U. Hirsch and W. D. Neumann, On cyclic branched coverings of spheres, Math. Ann. 215 (1975), 289–291. MR 375321, DOI 10.1007/BF01343895
José M. Montesinos, Surgery on links and double branched covers of $S^{3}$, Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R. H. Fox), Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N.J., 1975, pp. 227–259. MR 0380802
Robert Myers, Open book decompositions of $3$-manifolds, Proc. Amer. Math. Soc. 72 (1978), no. 2, 397–402. MR 507346, DOI 10.1090/S0002-9939-1978-0507346-5
Makoto Sakuma, Surface bundles over $S^{1}$ which are $2$-fold branched cyclic coverings of $S^{3}$, Math. Sem. Notes Kobe Univ. 9 (1981), no. 1, 159–180. MR 634005
Teruhiko Soma, Hyperbolic, fibred links and fibre-concordances, Math. Proc. Cambridge Philos. Soc. 96 (1984), no. 2, 283–294. MR 757661, DOI 10.1017/S0305004100062174
John R. Stallings, Constructions of fibred knots and links, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 55–60. MR 520522