2023/12/21 by Kokoro Tanaka, Tanaka, Kokoro, Yuta Taniguchi +1
Mathematics · Medicine · #57K10 #57K12 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2312.13679
openalex publication_date 2023/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The knot quandle is a complete invariant for oriented classical knots in the 3-sphere up to orientation. Eisermann computed the second quandle homology group of the knot quandle and showed that it characterizes the unknot. In this paper, we compute the second quandle homology group of the knot n-quandle completely, where the knot n-quandle is a certain quotient of the knot quandle for each integer n greater than one. Although the knot n-quandle is weaker than the knot quandle, the second quandle homology group of the former is found to have more information than that of the latter. As one of the consequences, it follows that the second quandle homology group of the knot 3-quandle characterizes the unknot, the trefoil and the cinquefoil.