Determinant of the crossing matrix of a braid

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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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2026-02-06
DOI
https://doi.org/10.1142/s0218216526500173
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Determinant of the crossing matrix of a braid

A. Shimizu
Journal of Knot Theory and Its Ramifications
Geometric and Algebraic Topology
article

Determinant of the crossing matrix of a braid

A. Shimizu
article en

Abstract

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].

Journal of Knot Theory and Its Ramifications
Ochanomizu University (JP)
Openalex Percentile: Top 60%
Geometric and Algebraic Topology
DOISourceOpenAlex
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Determinant of the crossing matrix of a braid — A. Shimizu · Journal of Knot Theory and Its Ramifications (2026) | TGRS Research Map | TGRS