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PreprintarXiv licencearXiv

The crossing matrix and the Burau matrix of pure braids

  • Ayaka Shimizu
  • Yoshiro Yaguchi
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Abstract

We show that the first derivative of the Burau matrix at t=1 coincides with the Laplacian of the crossing matrix for pure braids. We also discuss conjugacy invariants derived from these matrices.

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Cite

BibTeXRIS
BibTeX
@misc{shimizu2026crossing,
  title = {{The crossing matrix and the Burau matrix of pure braids}},
  author = {Ayaka Shimizu and Yoshiro Yaguchi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.29147},
  eprint = {2608.29147},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29147},
}
RIS
TY  - UNPB
TI  - The crossing matrix and the Burau matrix of pure braids
AU  - Ayaka Shimizu
AU  - Yoshiro Yaguchi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2608.29147
UR  - https://arxiv.org/abs/2608.29147
AB  - We show that the first derivative of the Burau matrix at t=1 coincides with the Laplacian of the crossing matrix for pure braids. We also discuss conjugacy invariants derived from these matrices.
ER  -