The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle

2021/04/27 by Inoue, Ayumu
#52B15 #57K12 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2104.13065

Abstract

A quandle is an algebraic system which excels at describing limited symmetries of a space. We introduce the concept of Schläfli quandles which are defined relating to chosen rotational symmetries of regular tessellations. On the other hand, quandles have a good chemistry with knot theory. Associated with a knot we have its knot quandle. We show that the knot quandle of the m-twist-spun trefoil is a central extension of the Schläfli quandle related to the regular tessellation \ 3, m \ in the sense of the Schläfli symbol if m ≥ 3.

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