4-Strand Burau is Unfaithful Modulo 5

Published 3 Oct 2023 in math.RT | (2310.02403v1)

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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