Work

Determinant of the OU matrix of a braid diagram

Year: 2024

Type: article

Abstract: In this paper, we define the over–under matrix (OU matrix) of a braid diagram and discuss how the OU matrix reflects the warping degree or the layeredness of the braid diagram, and show that the determinant of the OU matrix of a layered braid diagram is the product of the determinants of the layers. We also introduce invariants of positive braids which are derived from the OU matrix.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500051

Authors: Ayaka Shimizu, Yoshiro Yaguchi

Institutions: Osaka Metropolitan University, Maebashi Institute of Technology

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

Awards: Construction of a sequence of Hurwitz equivalence invariants for braid systems and its application to surface braids, 結び目の局所変形の研究