# Virtual quandle for links in lens spaces

## TL;DR

This paper introduces a virtual quandle invariant for links in lens spaces, which is essential and easily computable from band diagrams, improving upon traditional invariants.

## Contribution

The authors construct a virtual quandle for links in lens spaces with q=1, providing an essential invariant with straightforward presentation from band diagrams.

## Key findings

- Virtual quandle is an essential link invariant in lens spaces.
- Presentation of the virtual quandle can be derived from band diagrams.
- The invariant improves the computability over traditional fundamental quandles.

## Abstract

We construct a virtual quandle for links in lens spaces $L(p,q)$, with $q=1$. This invariant has two valuable advantages over an ordinary fundamental quandle for links in lens spaces: the virtual quandle is an essential invariant and the presentation of the virtual quandle can be easily written from the band diagram of a link.