Demonstrates a braid invariant based on crossing matrix determinants in braids, suggesting its significance in braid theory.
In this paper, we define a braid invariant, the purified determinant [Formula: see text] of a braid [Formula: see text], considering the determinant of the crossing matrix of a pure braid derived from [Formula: see text], and show that [Formula: see text] for any pair of [Formula: see text]-braids [Formula: see text] and [Formula: see text].
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A. Shimizu (2026) studied this question.
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