Knots in Virtually Fibered 3-Manifolds

A smooth orientable compact $3$-manifold $N$ is said to be virtually fibered if it admits a finite index covering $p\colon M \to N$ such that $M$ is fibered. Chrisman-Manturov recently showed how knots in fibered knot complements can be studied using virtual knot theory. It will be shown how the same technique can be used to study knots in manifolds which are not fibered but are virtually fibered.
The first example of a non-fibered virtually fibered $3$-manifold is due to Gabai. The example takes the form of a link complement which is not fibered but admits a two-to-one covering by a fibered link complement. The talk will begin by considered knots in fibered link complements and then build up to considering knots in the complement of Gabai's example. We will conclude with a preliminary report on a general theory of virtual covers for knots in compact orientable 3-manifolds.