Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting surface bundles in finite covers of hyperbolic closed
  3-manifolds   The main theorem of this article provides sufficient conditions for a degree
$d$ finite cover $M'$ of a hyperbolic 3-manifold $M$ to be a surface-bundle.
Let $F$ be an embedded, closed and orientable surface of genus $g$, close to a
minimal surface in the cover $M'$, splitting $M'$ into a disjoint union of $q$
handlebodies and compression bodies. We show that there exists a fiber in the
complement of $F$ provided that $d$, $q$ and $g$ satisfy some inequality
involving an explicit constant $k$ depending only on the volume and the
injectivity radius of $M$. In particular, this theorem applies to a Heegaard
splitting of a finite covering $M'$, giving an explicit lower bound for the
genus of a strongly irreducible Heegaard splitting of $M'$. Applying the main
theorem to the setting of a circular decomposition associated to a non trivial
homology class of $M$ gives sufficient conditions for this homology class to
correspond to a fibration over the circle. Similar methods lead also to a
sufficient condition for an incompressible embedded surface in $M$ to be a
fiber.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph