Circular characteristics and fibrations of hyperbolic closed 3-manifolds
  This article provides sufficient conditions for a closed hyperbolic 3-manifold $M$ with non zero first Betti number to fiber over the circle, and to find a fiber in $M$. Those conditions are formulated in terms of the behavior the circular characteristic in finite regular covers of $M$. We define the circular characteristic as an invariant associated to a non trivial cohomology class $\alpha$ of $M$, using a Heegaard characteristic. 
Claire Renard
math.GT