A manifold \(M\) is virtually fibered if there is a finite cover of \(M\) that is fibered. Thurston conjectured that a compact orientable irreducible 3-manifold whose fundamental group is infinite and contains no non-peripheral \({\mathbb Z}\times{\mathbb Z}\) subgroup is virtually fibered if all the boundary components of \(M\) are tori.
The author proves that every 2-bridge knot complement and non-trivial 2-bridge link complement is virtually fibered. The proof starts with the observation that a great circle link complement in \(S^3\) is fibered. The argument is completed by showing that every 2-bridge knot complement and non-trivial 2-bridge link complement has a covering which is a great circle link complement. For 2-bridge knots these coverings have also been studied previously by G. Burde [Kobe J. Math. 5, No. 2, 209–219 (1988; Zbl 0674.57007)] and are known as dihedral coverings.
The second main result of the article is that the complement of every spherical Montesinos knot or link is virtually fibered. The proof of this result uses a special case of Thurston’s orbifold theorem.
The author remarks that the 2-fold cover of \(S^3\), branched along a 2-bridge knot or non-trivial 2-bridge link is a spherical manifold (lens space). Hence the result about 2-bridge knots and links can also be proved by using the orbifold theorem. However, this is not a direct proof.