# Computing Ribbon Obstructions for Colored Knots

## TL;DR

This paper introduces an algorithm to compute Kjuchukova's $\\Xi_p$ invariant for Fox $p$-colored knots, aiding in detecting ribbon obstructions via dihedral branched covers, with example calculations included.

## Contribution

It provides a practical algorithm for evaluating the $\\Xi_p$ invariant directly from colored knot diagrams, facilitating ribbon obstruction analysis.

## Key findings

- Algorithm successfully computes $\\Xi_p$ from diagrams.
- Examples demonstrate the method's application.
- Supports analysis of ribbon obstructions in knot theory.

## 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.