A twisted link invariant derived from a virtual link invariant
Naoko Kamada
TL;DR
This paper introduces a new invariant for twisted links, extending virtual knot invariants to non-orientable surfaces using double coverings, and explores properties of these diagrams.
Contribution
It develops a twisted link invariant derived from the JKSS invariant of virtual links through double coverings, expanding the scope of link invariants.
Findings
The invariant can distinguish certain twisted links.
Properties of double covering diagrams are characterized.
The method extends virtual link invariants to non-orientable surfaces.
Abstract
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a possibly non-orientable surface. In this paper, we discuss an invariant of twisted links which is obtained from the JKSS invariant of virtual links by use of double coverings. We also discuss some properties of double covering diagrams.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Computational Geometry and Mesh Generation