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math.GT2026
The crossing matrix and the Burau matrix of pure braids
Ayaka Shimizu, Yoshiro Yaguchi
We show that the first derivative of the Burau matrix at coincides with the Laplacian of the crossing matrix for pure braids. We also discuss conjugacy invariants derived fro…
math.GT2026
Cabled braids and their crossing matrices
Ayaka Shimizu, Yoshiro Yaguchi
We study cabling operations on braids, and characterize the matrices that can be realized as crossing matrices of reducible pure braids. We also use cabling to construct enhanced c…
math.GT2026
Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence
Ayaka Shimizu, Yoshiro Yaguchi
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surfac…