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arXiv · 2509.08464

Determinant of the crossing matrix of a braid

Ayaka Shimizu
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Abstract

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 $b_2$.

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Ayaka Shimizu. 2025-09-21. Determinant of the crossing matrix of a braid. https://arxiv.org/abs/2509.08464

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