Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

Ayaka Shimizu; Yoshiro Yaguchi

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arXiv · 2601.02323

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

Ayaka Shimizu·Yoshiro Yaguchi

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Abstract

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 surface braids and surface links, we also define an invariant that can be used as an indicator of the necessity of Euler fusion or fission between braid systems.

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Ayaka Shimizu, Yoshiro Yaguchi. 2026-01-05. Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence. https://arxiv.org/abs/2601.02323

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