2025/05/26 by Gupta, Vaishnavi, Raundal, Hitesh
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2505.19573
The paper investigates biorderability of knot quandles of prime knots up to eight crossings. We prove that knot quandles of knots 63, 87, 88, 810 and 816 can not be biorderable. However, we see that knot quandles of knots 41, 61, 62, 76, 77, 81, 82, 83, 84, 85, 86, 89, 811, 812, 813, 814, 817, 818, 820 and 821 could be biorderable. We also give linear orders on the generating set of the knot quandle of a knot (among these knots) that could be extendable to biorders on the quandle.