Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2405.20159 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917940680458240 |
|---|---|
| author | Wang, Sike Wong, Helen |
| author_facet | Wang, Sike Wong, Helen |
| contents | The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative structure of the skein algebra is not well understood, with a priori exponential complexity. We consider the case of one-hole torus, and provide a polynomial algorithm for computing multiplication of any two skein elements. Some closed form formulas for multiplication of curves with low crossing number are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20159 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast Algorithm for Multiplication on the Skein Algebra of One-hole Torus Wang, Sike Wong, Helen Geometric Topology 57-08, 57K31, 57K16 The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative structure of the skein algebra is not well understood, with a priori exponential complexity. We consider the case of one-hole torus, and provide a polynomial algorithm for computing multiplication of any two skein elements. Some closed form formulas for multiplication of curves with low crossing number are also given. |
| title | Fast Algorithm for Multiplication on the Skein Algebra of One-hole Torus |
| topic | Geometric Topology 57-08, 57K31, 57K16 |
| url | https://arxiv.org/abs/2405.20159 |