Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.11569 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915874766585856 |
|---|---|
| author | Bosch, Boudewijn |
| author_facet | Bosch, Boudewijn |
| contents | The colored Jones polynomial associated to a knot admits an expansion of knot invariants known as the large-color expansion or Melvin-Morton-Rozansky expansion. We will show how this expansion can be derived from the universal invariant arising from a Hopf algebra $\mathbb{D}$, as introduced by Bar-Natan and Van der Veen. We utilize a Mathematica implementation to compute the universal invariant $\mathbf{Z}_{\mathbb{D}}(\mathcal{K})$ up to a certain order for a given knot $\mathcal{K}$, allowing for experimental verification of our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Large-Color Expansion Derived from the Universal Invariant Bosch, Boudewijn Geometric Topology Quantum Algebra 57K14, 16T05, 17B37 The colored Jones polynomial associated to a knot admits an expansion of knot invariants known as the large-color expansion or Melvin-Morton-Rozansky expansion. We will show how this expansion can be derived from the universal invariant arising from a Hopf algebra $\mathbb{D}$, as introduced by Bar-Natan and Van der Veen. We utilize a Mathematica implementation to compute the universal invariant $\mathbf{Z}_{\mathbb{D}}(\mathcal{K})$ up to a certain order for a given knot $\mathcal{K}$, allowing for experimental verification of our theoretical results. |
| title | The Large-Color Expansion Derived from the Universal Invariant |
| topic | Geometric Topology Quantum Algebra 57K14, 16T05, 17B37 |
| url | https://arxiv.org/abs/2411.11569 |