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

View PDF HTML (experimental) 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: 26 pages, 28 figures Subjects: Geometric Topology (math.GT); Group Theory (math.GR) MSC classes: 57M07, 57M10, 20F65 Cite as: arXiv:2607.05283 [math.GT] (or arXiv:2607.05283v1 [math.GT] for this version) https://doi.org/10.48550/arXiv.2607.05283 arXiv-issued DOI via DataCite Submission history From: Tara E. Brendle [view email] [v1] Mon, 6 Jul 2026 16:28:02 UTC (3,164 KB)