The Burau representation is faithful for n = 4

Vasudha Bharathram, Joan S. Birman, and Tara E. Brendle, arXiv:2607.05283 (version 2, September 2026), transcribed into PreTeXt from the PDF alone, and then built into every output PreTeXt makes.

The original is published by its authors under the Creative Commons Attribution 4.0 International License, and these derived versions are offered under the same license. Changes from the original: the text was transcribed into PreTeXt source and rebuilt, so the typography is PreTeXt's; items are numbered by PreTeXt (the unnumbered Main Theorem is Theorem 1.1, and Corollary 1.1 and Proposition 1.2 become 1.2 and 1.3); the bibliography is numbered in place of the original's alphabetic keys; several figures are cut into panels; one display of twenty terms is set on two lines. The words and the mathematics are the authors' own; we made no corrections of apparent errors or typos. The AMS-style PDF was compiled by hand from PreTeXt's LaTeX with one option added to a font package, a PreTeXt defect noted in the transcription's records.