Determinant of the OU matrix of a braid diagram

Ayaka Shimizu, Yoshiro Yaguchi

Published 2024-10-23Version 1

In this paper, we define the 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.