# Cyclic coverings of virtual link diagrams

## TL;DR

This paper introduces a method to construct mod m almost classical virtual link diagrams from any virtual link diagram, establishing a well-defined map and exploring applications of this construction.

## Contribution

It presents a new construction called m-fold cyclic covering diagram that produces mod m almost classical virtual links from arbitrary virtual links, ensuring well-definedness.

## Key findings

- The m-fold cyclic covering diagram is invariant under virtual link equivalence.
- A well-defined map from virtual links to mod m almost classical links is established.
- Applications of the construction are demonstrated.

## Abstract

A virtual link diagram is called mod $m$ almost classical if it admits an Alexander numbering valued in integers modulo $m$, and a virtual link is called mod $m$ almost classical if it has a mod $m$ almost classical diagram as a representative. In this paper, we introduce a method of constructing a mod $m$ almost classical virtual link diagram from a given virtual link diagram, which we call an $m$-fold cyclic covering diagram. The main result is that $m$-fold cyclic covering diagrams obtained from two equivalent virtual link diagrams are equivalent. Thus we have a well-defined map from the set of virtual links to the set of mod $m$ almost classical virtual links. Some applications are also given.