On hyperbolic surface bundles over the circle as branched double covers of the 3-sphere.

The branched virtual fibering theorem by Sakuma states that every closed orientable 3-manifold with a Heegaard surface of genus g has a branched double cover which is a genus g surface bundle over the circle. It is proved by Brooks that such a surface bundle can be chosen to be hyperbolic. We prove that the minimal entropy over all hyperbolic, genus g surface bundles as branched double covers of the 3-sphere behaves like 1/ g. We also give an alternative construction of surface bundles over the circle in Sakuma's theorem when closed 3-manifolds are branched double covers of the 3-sphere branched over links. A feature of surface bundles coming from our construction is that the monodromies can be read off the braids obtained from the links as the branched set. [ABSTRACT FROM AUTHOR]