Knot quandle decomposition along a torus
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909060323868672 |
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| author | Bonatto, Marco Cattabriga, Alessia Horvat, Eva |
| author_facet | Bonatto, Marco Cattabriga, Alessia Horvat, Eva |
| contents | We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of the paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12869 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Knot quandle decomposition along a torus Bonatto, Marco Cattabriga, Alessia Horvat, Eva Geometric Topology 57K10, 57K12, 57K14 We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of the paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained. |
| title | Knot quandle decomposition along a torus |
| topic | Geometric Topology 57K10, 57K12, 57K14 |
| url | https://arxiv.org/abs/2009.12869 |