A Perturbed-Alexander Invariant
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913315177889792 |
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| author | Bar-Natan, Dror van der Veen, Roland |
| author_facet | Bar-Natan, Dror van der Veen, Roland |
| contents | In this note we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant $ρ_1$ is not new, yet our formulas are by far the simplest and fastest: given a knot we write one of the standard matrices $A$ whose determinant is its Alexander polynomial, yet instead of computing the determinant we consider a certain quadratic expression in the entries of $A^{-1}$. The proximity of our formulas to the Alexander polynomial suggest that they should have a topological explanation. This we don't have yet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12298 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Perturbed-Alexander Invariant Bar-Natan, Dror van der Veen, Roland Geometric Topology Quantum Algebra 57K14, 16T99 In this note we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant $ρ_1$ is not new, yet our formulas are by far the simplest and fastest: given a knot we write one of the standard matrices $A$ whose determinant is its Alexander polynomial, yet instead of computing the determinant we consider a certain quadratic expression in the entries of $A^{-1}$. The proximity of our formulas to the Alexander polynomial suggest that they should have a topological explanation. This we don't have yet. |
| title | A Perturbed-Alexander Invariant |
| topic | Geometric Topology Quantum Algebra 57K14, 16T99 |
| url | https://arxiv.org/abs/2206.12298 |