English

4-Strand Burau is Unfaithful Modulo 5

Representation Theory 2023-10-05 v1

Abstract

We introduce a new algorithm for finding kernel elements in the Burau representation. Our algorithm applies reservoir sampling to a statistic on matrices which is closely correlated with Garside length. Using this we exhibit an explicit kernel element in the Burau representation on 4-strands reduced modulo 5.

Cite

@article{arxiv.2310.02403,
  title  = {4-Strand Burau is Unfaithful Modulo 5},
  author = {Joel Gibson and Geordie Williamson and Oded Yacobi},
  journal= {arXiv preprint arXiv:2310.02403},
  year   = {2023}
}

Comments

10 pages, 5 figures

R2 v1 2026-06-28T12:39:53.575Z