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arXiv · 2310.02403

4-Strand Burau is Unfaithful Modulo 5

Joel Gibson·Geordie Williamson·Oded Yacobi
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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.

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BibTeXRIS

Joel Gibson, Geordie Williamson, Oded Yacobi. 2023-10-03. 4-Strand Burau is Unfaithful Modulo 5. https://arxiv.org/abs/2310.02403

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