The clock theorem for knotoids and linkoids
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908559238758400 |
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| author | Gügümcü, Neslihan Kauffman, Louis H. |
| author_facet | Gügümcü, Neslihan Kauffman, Louis H. |
| contents | In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in $S^2$. The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many invariants of knotoids and linkoids including the Alexander polynomial, Mock Alexander polynomial and the Jones polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The clock theorem for knotoids and linkoids Gügümcü, Neslihan Kauffman, Louis H. Geometric Topology Combinatorics In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in $S^2$. The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many invariants of knotoids and linkoids including the Alexander polynomial, Mock Alexander polynomial and the Jones polynomial. |
| title | The clock theorem for knotoids and linkoids |
| topic | Geometric Topology Combinatorics |
| url | https://arxiv.org/abs/2509.21568 |