Knot-theoretic flocks

Maciej Niebrzydowski; Agata Pilitowska; Anna Zamojska-Dzienio

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arXiv · 1908.09954

Knot-theoretic flocks

Maciej Niebrzydowski·Agata Pilitowska·Anna Zamojska-Dzienio

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Abstract

We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We note that the operation used in knot-theoretic flocks has its non-associative version in extra loops. We use a group action on the set of flock colorings to improve the cocycle invariant associated with the knot-theoretic flock (co)homology.

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BibTeX RIS

Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio. 2019-08-26. Knot-theoretic flocks. https://arxiv.org/abs/1908.09954

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