Criteria for virtual fibering

We prove that an irreducible 3‐manifold with fundamental group that satisfies a certain group‐theoretic property called RFRS is virtually fibered. As a corollary, we show that 3‐dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut‐sutured compression body has a finite‐sheeted cover with a depth one taut‐oriented foliation.