Some computational results on mod 2 finite-type invariants of knots and string links

TL;DR

This paper provides a comprehensive table of primitive finite-type invariants for knots with up to ten crossings, explores mod-2 congruences, and presents computational results on 2-strand string links, advancing understanding of knot invariants.

Contribution

It offers the first extensive table of low-order finite-type invariants for small knots and reveals new mod-2 congruences and a chirality criterion, along with computational insights on string links.

Findings

Primitive invariants table for knots ≤10 crossings

Identification of mod-2 congruences and chirality criterion

Computational results on 2-strand string links

Abstract

We publish a table of primitive finite-type invariants of order less than or equal to six, for knots of ten or fewer crossings. We note certain mod-2 congruences, one of which leads to a chirality criterion in the Alexander polynomial. We state a computational result on mod-2 finite-type invariants of 2-strand string links.