A perturbed Alexander polynomial for singular knots

2024/09/26 by Schut, Martine, van der Veen, Roland
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2409.17657

Abstract

We introduce a version of the Alexander polynomial for singular knots and tangles and show how it can be strengthened considerably by introducing a perturbation. For singular long knots, we also prove that our Alexander polynomial agrees with previous definitions.

Related

• Explicit Formulas for the Alexander Polynomial of Pretzel Knots
• Alexander polynomials of ribbon knots and virtual knots
• The Jones and Alexander polynomials for singular links
• Twisted Knots and the Perturbed Alexander Invariant
• A Perturbed-Alexander Invariant