Converting virtual link diagrams to normal ones

TL;DR

This paper introduces a method to convert virtual link diagrams into normal ones using double covering, ensuring the resulting diagrams are related by known moves, thus aiding in the study of virtual links.

Contribution

The paper presents a novel double covering technique for converting virtual link diagrams into normal diagrams, preserving equivalence through generalized Reidemeister moves and Kauffman flypes.

Findings

The method successfully converts virtual link diagrams into normal diagrams.

Converted diagrams are related by generalized Reidemeister moves and Kauffman flypes.

The approach enhances understanding of virtual link equivalence.

Abstract

A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering technique. We show that the normal virtual link diagrams obtained from two equivalent virtual link diagrams are related by generalized Reidemeister moves and Kauffman flypes.