Determinant of the OU matrix of a braid diagram

Ayaka Shimizu; Yoshiro Yaguchi

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arXiv · 2410.17778

Determinant of the OU matrix of a braid diagram

Ayaka Shimizu·Yoshiro Yaguchi

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Abstract

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.

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Ayaka Shimizu, Yoshiro Yaguchi. 2024-10-23. Determinant of the OU matrix of a braid diagram. https://arxiv.org/abs/2410.17778

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