Criteria for virtual fibering

TL;DR

This paper establishes criteria for when certain 3-manifolds are virtually fibered, linking group-theoretic properties to topological fiberings, with applications to orbifolds and sutured manifolds.

Contribution

It proves that RFRS group properties imply virtual fibering of 3-manifolds and applies this to specific orbifolds and sutured compression bodies.

Findings

Irreducible 3-manifolds with RFRS groups are virtually fibered.

Certain orbifolds, including Bianchi and Seifert Weber spaces, virtually fiber.

Taut sutured compression bodies have finite covers with depth one taut foliations.

Abstract

We prove that an irreducible 3-manifold whose fundamental group 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 orbifolds. Moreover, we show that a taut sutured compression body has a finite-sheeted cover with a depth one taut-oriented foliation.