On the Aicardi-Juyumaya bracket for tied links
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912621387579392 |
|---|---|
| author | Cárdenas-Andaur, O'Bryan |
| author_facet | Cárdenas-Andaur, O'Bryan |
| contents | Given a tied link $L$, the invariant $\langle\langle\cdot\rangle\rangle$ generalizes the Kauffman bracket of classical links. However, the analogues of Kauffman states and their relationship to this invariant are not immediately clear. We address this question by defining the Aicardi-Juyumaya states, and show that the contribution of each AJ-state to $\langle\langle\cdot\rangle\rangle$ does not depend on the chosen resolution tree. We also present an algorithm to compute the double bracket of a tied link diagram, and use it to find pairs of examples of (oriented) tied links sharing the same Homflypt polynomial but different tied Jones polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Aicardi-Juyumaya bracket for tied links Cárdenas-Andaur, O'Bryan Geometric Topology 57K10, 57K12, 57K14 Given a tied link $L$, the invariant $\langle\langle\cdot\rangle\rangle$ generalizes the Kauffman bracket of classical links. However, the analogues of Kauffman states and their relationship to this invariant are not immediately clear. We address this question by defining the Aicardi-Juyumaya states, and show that the contribution of each AJ-state to $\langle\langle\cdot\rangle\rangle$ does not depend on the chosen resolution tree. We also present an algorithm to compute the double bracket of a tied link diagram, and use it to find pairs of examples of (oriented) tied links sharing the same Homflypt polynomial but different tied Jones polynomial. |
| title | On the Aicardi-Juyumaya bracket for tied links |
| topic | Geometric Topology 57K10, 57K12, 57K14 |
| url | https://arxiv.org/abs/2411.06259 |