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.

中文翻译：

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结区着色层和更高的差异

我们使用三元拟群归纳地定义了打结和打结曲面图的着色层。来自这种着色系统的同源不变量使用更短的差异和比标准同源差异更高的程度，并提供通常更复杂的同源群。