4-strand Burau is unfaithful modulo 5

Joel Gibson; Geordie Williamson; Oded Yacobi

4-strand Burau is unfaithful modulo 5

Authors

Joel Gibson Sydney Mathematical Research Institute
Geordie Williamson University of Sydney https://orcid.org/0000-0003-3672-5284
Oded Yacobi University of Sydney https://orcid.org/0000-0002-4739-0689

Keywords:

Braid Group, Burau Representation, Garside Normal Form, Reservoir Sampling

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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Published

02/28/2025

How to Cite

Gibson, J., Williamson, G., & Yacobi, O. (2025). 4-strand Burau is unfaithful modulo 5. Journal of Experimental Mathematics, 1(1), 36–50. Retrieved from https://jexpmath.org/index.php/jem/article/view/Vol-1Issue-1Paper-3