On 3-manifolds having surface bundles as branched coverings

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.