
TL;DR
This paper employs virtual knot theory to identify non-invertibility in classical links within three-dimensional space, leveraging virtual covers associated with fibered and virtually fibered links to detect symmetries.
Contribution
It introduces a novel application of virtual knot theory to analyze the invertibility of classical links via virtual covers, especially for links related to fibered and virtually fibered links.
Findings
Virtual covers can detect non-invertibility of classical links.
Symmetry conditions on virtual knots relate to link invertibility.
Virtual covers extend to links with virtually fibered components.
Abstract
We use virtual knot theory to detect the non-invertibility of some classical links in . These links appear in the study of virtual covers. Briefly, a virtual cover associates a virtual knot to a knot in a -manifold , under certain hypotheses on and . Virtual covers of links in come from taking to be in the complement of a fibered link . If is invertible and is "close to" a fiber of , then satisfies a symmetry condition to which some virtual knot polynomials are sensitive. We also discuss virtual covers of links where is not fibered but is virtually fibered (in the sense of W. Thurston).
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