Rigidity of highly twisted plat diagrams
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913982897455104 |
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| author | Lazarovich, Nir Moriah, Yoav Pinsky, Tali Purcell, Jessica S. |
| author_facet | Lazarovich, Nir Moriah, Yoav Pinsky, Tali Purcell, Jessica S. |
| contents | In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least four, and height at least two, and each twist region of the plat contains at least four crossings, then such a projection is unique up to obvious rotations. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of highly twisted plat diagrams Lazarovich, Nir Moriah, Yoav Pinsky, Tali Purcell, Jessica S. Geometric Topology 57K10, 57K32, 20F36 In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a $2m$-plat projection, where $m$ is at least four, and height at least two, and each twist region of the plat contains at least four crossings, then such a projection is unique up to obvious rotations. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links. |
| title | Rigidity of highly twisted plat diagrams |
| topic | Geometric Topology 57K10, 57K32, 20F36 |
| url | https://arxiv.org/abs/2508.07303 |