Orderability of knot quandles

Hitesh Raundal, Mahender Singh, Manpreet Singh

Published 2020-10-14Version 1

The paper develops a general theory of orderability of quandles with a focus on link quandles of tame links. We prove that knot quandles of many fibered prime knots are right-orderable, whereas link quandles of many non-trivial torus links are not right-orderable. As a consequence, we deduce that the knot quandle of the trefoil is neither left nor right orderable. Further, it is proved that link quandles of certain non-trivial positive (or negative) links are not bi-orderable, which includes some alternating knots of prime determinant and alternating Montesinos links. The paper also explores interconnections between orderability of quandles and that of their enveloping groups. The results show that orderability of link quandles behave quite differently than that of corresponding link groups.