From planar to annular to toroidal bracket polynomials for pseudo knots and links
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916906916642816 |
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| author | Diamantis, Ioannis Lambropoulou, Sofia Mahmoudi, Sonia |
| author_facet | Diamantis, Ioannis Lambropoulou, Sofia Mahmoudi, Sonia |
| contents | Pseudo links are equivalence classes under Reidemeister-type moves of link diagrams containing crossings with undefined over and under information. In this paper, we extend the Kauffman bracket and Jones-type polynomials from planar pseudo links to annular and toroidal pseudo links and their respective lifts from the three-space to the solid torus and the thickened torus. Moreover, since annular and toroidal pseudo links can be represented as mixed links in the three-sphere, we also introduce the respective Kauffman bracket and Jones-type polynomials for their planar mixed link diagrams. Our work provides new tools for the study of annular and toroidal pseudo links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From planar to annular to toroidal bracket polynomials for pseudo knots and links Diamantis, Ioannis Lambropoulou, Sofia Mahmoudi, Sonia Geometric Topology 57K10, 57K12, 57K14, 57K31, 57K35 Pseudo links are equivalence classes under Reidemeister-type moves of link diagrams containing crossings with undefined over and under information. In this paper, we extend the Kauffman bracket and Jones-type polynomials from planar pseudo links to annular and toroidal pseudo links and their respective lifts from the three-space to the solid torus and the thickened torus. Moreover, since annular and toroidal pseudo links can be represented as mixed links in the three-sphere, we also introduce the respective Kauffman bracket and Jones-type polynomials for their planar mixed link diagrams. Our work provides new tools for the study of annular and toroidal pseudo links. |
| title | From planar to annular to toroidal bracket polynomials for pseudo knots and links |
| topic | Geometric Topology 57K10, 57K12, 57K14, 57K31, 57K35 |
| url | https://arxiv.org/abs/2501.00736 |