The shadow quandle cocycle invariant of knotoids

2022/07/05 by Nicholas Cazet, Cazet, Nicholas
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Numerical Analysis Techniques #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2207.02330

openalex publication_date 2022/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 3₁ 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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