A presentation for the category of $sl(3)$ webs and an extension of the quantum $sl(3)$-invariant to tangles
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914007980441600 |
|---|---|
| author | Amarasinghe, Nipun |
| author_facet | Amarasinghe, Nipun |
| contents | We extend the $sl(3)$-polynomial invariant for links to tangles. Motivated by Kuperberg's construction of this invariant via planar trivalent graphs, we first define a category of $sl(3)$ webs and its sister linear category, and describe them via generators and relations. Then we define a functor from the category of oriented tangles to the linear category of $sl(3)$ webs, which yields an invariant for tangles and allows us to recover the $sl(3)$-polynomial invariant for links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A presentation for the category of $sl(3)$ webs and an extension of the quantum $sl(3)$-invariant to tangles Amarasinghe, Nipun Geometric Topology 57K12 (Primary), 18M05 (Secondary) We extend the $sl(3)$-polynomial invariant for links to tangles. Motivated by Kuperberg's construction of this invariant via planar trivalent graphs, we first define a category of $sl(3)$ webs and its sister linear category, and describe them via generators and relations. Then we define a functor from the category of oriented tangles to the linear category of $sl(3)$ webs, which yields an invariant for tangles and allows us to recover the $sl(3)$-polynomial invariant for links. |
| title | A presentation for the category of $sl(3)$ webs and an extension of the quantum $sl(3)$-invariant to tangles |
| topic | Geometric Topology 57K12 (Primary), 18M05 (Secondary) |
| url | https://arxiv.org/abs/2506.11301 |