Determinant of the OU matrix of a braid diagram

Ayaka Shimizu; Yoshiro Yaguchi

Determinant of the OU matrix of a braid diagram

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arxiv 2410.17778 v2 pith:5BARHQBM submitted 2024-10-23 math.GT

Ayaka Shimizu , Yoshiro Yaguchi This is my paper · ORCID

classification math.GT

keywords matrixbraiddiagramdeterminantbraidsdefinedegreederived

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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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Orbits by the up-down action of braid diagrams
math.GT 2024-12 conditional novelty 6.0 of 10

The orbits of the up-down action of classical and virtual braid diagrams on Z^n are completely determined: trace alone for virtual braids, trace plus a parity-type count for classical braids.

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