A non-Haken hyperbolic 3-manifold covered by a surface bundle (Q1891202)

The question as to whether a finite volume hyperbolic 3-manifold has a finite cover which fibers over the circle, seems at present completely mysterious. In this paper we give the first explicit examples of non- Haken hyperbolic 3-manifolds covered by a manifold that fibers of the circle. The methods used are arithmetic using the theory of quaternion algebras.