Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex