The CN matrix of a pure braid projection
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913998456225792 |
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| author | Ozawa, Yuko Shimizu, Ayaka Yaguchi, Yoshiro |
| author_facet | Ozawa, Yuko Shimizu, Ayaka Yaguchi, Yoshiro |
| contents | The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, several patterns of an $n \times n$ matrix to be a CN matrix are discussed, and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The CN matrix of a pure braid projection Ozawa, Yuko Shimizu, Ayaka Yaguchi, Yoshiro Geometric Topology The CN matrix of an $n$-braid projection $B$ is an $n \times n$ matrix such that each $(i,j)$ entry indicates the number of crossings between $i^{th}$ and $j^{th}$ strands of $B$. In this paper, several patterns of an $n \times n$ matrix to be a CN matrix are discussed, and the CN matrix of a pure 6-braid projection is characterized. As an application, the OU matrix of a pure 6-braid diagram and the crossing matrix of a positive pure 6-braid are also characterized. |
| title | The CN matrix of a pure braid projection |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2506.08659 |