The shadow quandle cocycle invariant of knotoids

Nicholas Cazet

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arXiv · 2207.02330

The shadow quandle cocycle invariant of knotoids

Nicholas Cazet

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Abstract

This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle invariant is shown to distinguish infinitely many knotoids from their mirrors. Specifically, the knot-type knotoid $3_1$ is shown to be chiral. The weight of a quandle 3-cocycle is used to calculate the crossing numbers of infinitely many multi-linkoids.

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Nicholas Cazet. 2022-07-05. The shadow quandle cocycle invariant of knotoids. https://arxiv.org/abs/2207.02330

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