Determinant of the crossing matrix of a braid

Journal of Knot Theory and Its Ramifications 2026 Open access

Read full text
Authors: A. Shimizu
DOI: 10.1142/s0218216526500173
Cited by: 0
References: 8

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].

Fields of Study & Subjects

Geometric and Algebraic Topology Advanced Combinatorial Mathematics Homotopy and Cohomology in Algebraic Topology

Publication details

Journal / source
Journal of Knot Theory and Its Ramifications
Volume
35
Issue
10
Publication date
6 February 2026
Language
EN