2018/09/29 by Susumu Hirose, Hirose, Susumu, Eiko Kin +1
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT
paper · pdf · doi:10.48550/arxiv.1810.00212
10 pages, 8 figures; minor changes from previous version
arxiv created 2019/08/27 · arxiv updated 2019/08/28
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.