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 $m \geq 3$.
Acknowledgments
The author wishes to express his gratitude to the referee for his/her invaluable comments. He is supported by JSPS KAKENHI Grant Numbers JP16K17591 and JP19K03476 partially.
Citation
Ayumu Inoue. "The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle." Osaka J. Math. 60 (3) 597 - 611, July 2023.