Computing ribbon obstructions for colored knots
Volume 253 / 2021
Fundamenta Mathematicae 253 (2021), 155-173
MSC: Primary 57M12; Secondary 57K10, 57N70.
DOI: 10.4064/fm767-7-2020
Published online: 26 November 2020
Abstract
Kjuchukova’s $\varXi _p$ invariant gives a ribbon obstruction for Fox $p$-colored knots. The invariant is derived from dihedral branched covers of 4-manifolds, and can be used to calculate the signatures of these covers when singularities on the branching sets are present. In this note, we give an algorithm for evaluating $\varXi _p$ from a colored knot diagram, and compute a couple of examples.
