A perturbed-Alexander invariant
Dror Bar-Natan
University of Toronto, Toronto, Ontario, CanadaRoland van der Veen
University of Groningen, AK Groningen, The Netherlands
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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 is not new; yet our formulas are by far the simplest and fastest. Given a knot, we write one of the standard matrices, , whose determinant is its Alexander polynomial; yet instead of computing the determinant, we consider a certain quadratic expression in the entries of . The proximity of our formulas to the Alexander polynomial suggests that they should have a topological explanation, which we do not have yet.
Cite this article
Dror Bar-Natan, Roland van der Veen, A perturbed-Alexander invariant. Quantum Topol. (2024), published online first
DOI 10.4171/QT/206