A Perturbed-Alexander Invariant

Dror Bar-Natan; Roland van der Veen

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arXiv · 2206.12298

A Perturbed-Alexander Invariant

Dror Bar-Natan·Roland van der Veen

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Abstract

In this note we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant $\rho_1$ 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.

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Dror Bar-Natan, Roland van der Veen. 2022-06-24. A Perturbed-Alexander Invariant. https://arxiv.org/abs/2206.12298

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