Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.01629 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Braidoids form a counterpart theory to the theory of planar knotoids, just as braids do for three-dimensional links. As such, planar knotoid diagrams represent the same knotoid in $\mathbb{R}^2$ if and only if they can be presented as the closure of two labeled braidoid diagrams related by an equivalence relation, named $L$-equivalence. In this paper, we refine the notion of $L$-equivalence of braidoid diagrams in order to obtain an equivalence theorem for (multi)-knotoid diagrams in $S^2$ when represented as the closure of labeled braidoid diagrams.