Virtual covers of links

Abstract

We use virtual knot theory to detect the non-invertibility of some classical links in [Formula: see text]. These links appear in the study of virtual covers. Briefly, a virtual cover associates a virtual knot [Formula: see text] to a knot [Formula: see text] in a [Formula: see text]-manifold [Formula: see text], under certain hypotheses on [Formula: see text] and [Formula: see text]. Virtual covers of links in [Formula: see text] come from taking [Formula: see text] to be in the complement [Formula: see text] of a fibered link [Formula: see text]. If [Formula: see text] is invertible and [Formula: see text] is “close to” a fiber of [Formula: see text], then [Formula: see text] satisfies a symmetry condition to which some virtual knot polynomials are sensitive. We also discuss virtual covers of links [Formula: see text], where [Formula: see text] is not fibered, but is virtually fibered (in the sense of W. Thurston).