Filamentations for Virtual Links

TL;DR

This paper extends filamentation invariants from virtual knots to virtual links, providing new tools to detect non-classical virtual links and demonstrating their effectiveness with specific examples.

Contribution

It generalizes filamentation techniques to multi-component virtual links and offers new methods for identifying non-classical virtual links.

Findings

Filamentation invariants can detect non-classical virtual links.

Extension of filamentation techniques from knots to links.

Examples demonstrate the effectiveness of the new methods.

Abstract

In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial. A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used to detect non-classical virtual knots. We extend these filamentation techniques to virtual links with more than one component. We also give examples of virtual links that they can detect as non-classical.