Virtually Haken fillings and semi-bundles

Abstract

Suppose that $M$ is a fibered three-manifold whose fiber is a surface of positive genus with one boundary component. Assume that $M$ is not a semi-bundle. We show that infinitely many fillings of $M$ along $\partial M$ are virtually Haken. It follows that infinitely many Dehn-surgeries of any non-trivial knot in the three-sphere are virtually Haken.