[2607.05283] The Burau representation of the braid group is faithful for n = 4

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arXiv:2607.05283 (math)

[Submitted on 6 Jul 2026]

Title:The Burau representation of the braid group is faithful for n = 4

Authors:Vasudha Bharathram, Joan S. Birman, Tara E. Brendle<br>View a PDF of the paper titled The Burau representation of the braid group is faithful for n = 4, by Vasudha Bharathram and 2 other authors

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Abstract:In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for n = 4. An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.

Comments:<br>26 pages, 28 figures

Subjects:

Geometric Topology (math.GT); Group Theory (math.GR)

MSC classes:<br>57M07, 57M10, 20F65

Cite as:<br>arXiv:2607.05283 [math.GT]

(or<br>arXiv:2607.05283v1 [math.GT] for this version)

https://doi.org/10.48550/arXiv.2607.05283

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arXiv-issued DOI via DataCite

Submission history<br>From: Tara E. Brendle [view email]<br>[v1]<br>Mon, 6 Jul 2026 16:28:02 UTC (3,164 KB)

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