Computing Ribbon Obstructions for Colored Knots

Abstract

Kjuchukova's ${\Xi }_p$ invariant gives a ribbon obstruction for Fox $p$-colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and is needed to calculate the signatures of these covers, when singularities on the branching sets are present. In this note, we give an algorithm for evaluating ${\Xi }_p$ from a colored knot diagram, and compute a couple of examples.

14 pages. 0 footnotes. Changes to exposition and new example. To appear in Fundamenta Mathematicae. Originally part of arXiv:1710.11562