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arXiv:2607.05283math.GT

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

Vasudha Bharathram, Joan S. Birman, Tara E. Brendle

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.

arXiv comments
28 pages, 32 figures. Minor corrections and improved exposition
Journal reference
DOI
Subjects
math.GTGeometric Topology math.GRGroup Theory

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Sep 2026 to Sep 2026. Found in 1 HN submission from Jul 2026 to Jul 2026. Open submission discussions.

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    • Gift link: https://www.nytimes.com/2026/09/06/science/92-year-old-mathe... This is a really cool story. Joan Birman is 99 now and her apprentice Vasudha Bharathram, a 15 y/o high school student at the time, is now a graduate student at Princeton, originally accepted on a…

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