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The shadow quandle cocycle invariant of knotoids

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arxiv 2207.02330 v2 pith:YIJ5EP6L submitted 2022-07-05 math.GT math.AT

Nicholas Cazet This is my paper · ORCID
classification math.GTmath.AT
keywords quandleshadowcocycleinvariantknotoidsinfinitelymanycalculate
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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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