Criteria for virtual fibering

We prove that an irreducible 3-manifold with fundamental groupthat satisfies a certain group-theoretic property called RFRSis virtually fibered. As a corollary, we show that 3-dimensionalreflection orbifolds and arithmetic hyperbolic orbifolds definedby a quadratic form virtually fiber. These include the SeifertWeber dodecahedral space and the Bianchi groups. Moreover, weshow that a taut-sutured compression body has a finite-sheetedcover with a depth one taut-oriented foliation. Received July 29, 2007.