Determinant of the crossing matrix of a braid
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908548940693504 |
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| author | Shimizu, Ayaka |
| author_facet | Shimizu, Ayaka |
| contents | In this paper, we define a braid invariant, the purified determinant $P(b)$ of a braid $b$, considering the determinant of the crossing matrix of a pure braid derived from $b$, and show that $P(b_1 b_2)=P(b_2 b_1)$ for any pair of $n$-braids $b_1$ and $b_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determinant of the crossing matrix of a braid Shimizu, Ayaka Geometric Topology In this paper, we define a braid invariant, the purified determinant $P(b)$ of a braid $b$, considering the determinant of the crossing matrix of a pure braid derived from $b$, and show that $P(b_1 b_2)=P(b_2 b_1)$ for any pair of $n$-braids $b_1$ and $b_2$. |
| title | Determinant of the crossing matrix of a braid |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.08464 |