On the knot quandle of the twist-spun trefoil

2018/08/20 by Ayumu Inoue, Inoue, Ayumu
Mathematics · #52B15 #57Q45 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1808.06276

openalex publication_date 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the knot quandle of the 3-, 4-, or 5-twist-spun trefoil is isomorphic to a quandle related to the 16-, 24-, or 600-cell respectively. We further show that the cardinality of the knot quandle of the m-twist-spun trefoil is finite if and only if 1 ≤ m ≤ 5. This phenomenon is attributable to the fact that the regular tessellation \ 3, m \, in the sense of the Schläfli symbol, consists of infinite triangles if m is greater than or equal to 6.

Citations

• A classifying invariant of knots, the knot quandle

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