Orderability of knot quandles.
Orderability of knot quandles.
复制标题
结问题的可排序性。
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Manpreet Singh
中科院分区：
文献类型：
--
作者：
Hitesh Raundal;Mahender Singh;Manpreet Singh
本文发展了困境的一般可排序性理论，重点研究了驯服链接的链接困境。我们证明了许多纤维素数纽结的纽结困境是右可序的，而许多非平凡环面环的链环困境是不可右序的。因此，我们推论三叶草的纽结既不是左的，也不是右的。进一步，证明了某些非平凡正(负)环的环困境是不可双序的，其中包括一些素数行列式和交错Montesinos环的交错纽结。本文还探讨了对偶的可排序性与其包络群的可排序性之间的内在联系。结果表明，链环的有序性与相应链组的有序性有很大的不同。
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.