Virtual Knotoids in Thickened Surfaces

TL;DR

This paper introduces a geometric interpretation of virtual knotoids as arcs in thickened surfaces, demonstrating that virtual knotoid theory generalizes classical knotoid theory and confirming a conjecture by Kauffman and the first author.

Contribution

It provides a geometric framework for virtual knotoids and proves their relation to classical knotoids, confirming a longstanding conjecture.

Findings

Virtual knotoids are arcs in thickened surfaces.

Virtual knotoid theory generalizes classical knotoid theory.

Confirmed a conjecture of Kauffman and the first author.

Abstract

In this paper, we give a geometric interpretation of virtual knotoids as arcs in thickened surfaces. Then we show that virtual knotoid theory is a generalization of classical knotoid theory. This gives a proof of a conjecture of Kauffman and the first author.