A Practical Algorithm for Knot Factorisation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917977497010176 |
|---|---|
| author | He, Alexander Sedgwick, Eric Spreer, Jonathan |
| author_facet | He, Alexander Sedgwick, Eric Spreer, Jonathan |
| contents | We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inputs of reasonable size, including prime knots from the $19$-crossing census. The main new ingredient in this work is an object that we call an "edge-ideal triangulation", which is what our algorithm uses to represent knots. As other applications, we give an alternative proof that prime knot recognition is in coNP, and present some new complexity results for triangulations. Beyond knots, our work showcases edge-ideal triangulations as a tool for potential applications in $3$-manifold topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Practical Algorithm for Knot Factorisation He, Alexander Sedgwick, Eric Spreer, Jonathan Geometric Topology Computational Geometry 57K10, 57-04 We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inputs of reasonable size, including prime knots from the $19$-crossing census. The main new ingredient in this work is an object that we call an "edge-ideal triangulation", which is what our algorithm uses to represent knots. As other applications, we give an alternative proof that prime knot recognition is in coNP, and present some new complexity results for triangulations. Beyond knots, our work showcases edge-ideal triangulations as a tool for potential applications in $3$-manifold topology. |
| title | A Practical Algorithm for Knot Factorisation |
| topic | Geometric Topology Computational Geometry 57K10, 57-04 |
| url | https://arxiv.org/abs/2504.03942 |