# Layers of knot region colorings and higher differentials

## TL;DR

This paper introduces a new layered coloring method for knot diagrams using ternary quasigroups, leading to advanced homological invariants with more complex structures than traditional approaches.

## Contribution

It develops an inductive layering technique for colorings that results in higher-degree differentials, enhancing the complexity of homology groups in knot theory.

## Key findings

- New layered coloring framework for knots
- Homological invariants with higher-degree differentials
- Access to more complex homology groups

## Abstract

We inductively define layers of colorings of knot and knotted surface diagrams using ternary quasigroups. Homological invariants from such systems of colorings use shorter differentials and of higher degree than the standard homology differentials, and give access to typically more complex homology groups.