Coherent double coverings of virtual link diagrams

TL;DR

This paper introduces a method to convert virtual link diagrams into normal virtual links, preserving equivalence and exploring their properties and invariants, bridging concepts between virtual and classical link theories.

Contribution

The paper presents a novel method for converting virtual link diagrams into normal virtual links and analyzes its relationship with virtual link invariants.

Findings

Converted diagrams are equivalent if original diagrams are equivalent

The method preserves virtual link invariants

Normal virtual links share properties with classical links

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. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram. We show that the normal virtual link diagrams obtained by this method from two equivalent virtual link diagrams are equivalent. We discuss the relationship between this method and some invariants of virtual links.