Dynnikov coordinates on virtual braid groups

TL;DR

This paper introduces Dynnikov coordinates for virtual braid groups, proving their faithfulness for virtual 2-braids and suggesting they are highly effective invariants for all virtual braids.

Contribution

The paper defines Dynnikov coordinates for virtual braid groups and establishes their faithfulness for virtual 2-braids, proposing their potential as powerful invariants.

Findings

Dynnikov coordinates are faithful for virtual 2-braids.

Evidence suggests they are effective for general virtual braids.

Potential for these coordinates to serve as strong invariants.

Abstract

We define Dynnikov coordinates on virtual braid groups. We prove that they are faithful invariants of virtual 2-braids, and present evidence that they are also very powerful invariants for general virtual braids.