A non-haken hyperbolic 3-manifold covered by a surface bundle

Abstract

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. © 1995 by Pacific Journal of Mathematics.