Work

Determinant of the crossing matrix of a braid

Year: 2026

Type: article

Abstract: In this paper, we define a braid invariant, the purified determinant [Formula: see text] of a braid b, considering the determinant of the crossing matrix of a pure braid derived from b, and show that [Formula: see text] for any pair of n-braids [Formula: see text] and [Formula: see text].

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216526500173

Author: Ayaka Shimizu

Institution: Ochanomizu University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W7128023283

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Cites: 8

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