Orderability of link quandles
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866915556202905600 |
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| author | Raundal, Hitesh Singh, Mahender Singh, Manpreet |
| author_facet | Raundal, Hitesh Singh, Mahender Singh, Manpreet |
| contents | The paper develops a general theory of orderability of quandles with a focus on link quandles of tame links and gives some general constructions of orderable quandles. We prove that knot quandles of many fibered prime knots are right-orderable, whereas link quandles of most 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 establish that orderability of link quandles behave quite differently than that of corresponding link groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_07159 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Orderability of link quandles Raundal, Hitesh Singh, Mahender Singh, Manpreet Geometric Topology 2020: Primary 57K10, Secondary 57K12 The paper develops a general theory of orderability of quandles with a focus on link quandles of tame links and gives some general constructions of orderable quandles. We prove that knot quandles of many fibered prime knots are right-orderable, whereas link quandles of most 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 establish that orderability of link quandles behave quite differently than that of corresponding link groups. |
| title | Orderability of link quandles |
| topic | Geometric Topology 2020: Primary 57K10, Secondary 57K12 |
| url | https://arxiv.org/abs/2010.07159 |