Mathematicians Prove the Burau Representation is Faithful for n = 4
The Burau representation of the braid group is faithful for n = 4
We have finally proven that the Burau representation of the classical braid group is faithful for n equals 4. Building on earlier ideas from Moody, Long, Long-Paton, and Bigelow, our work confirms this long-standing conjecture. This result immediately implies that the Jones representation of the braid group is also faithful for n equals 4, resolving a significant question in geometric topology and group theory.
An immediate corollary is that the Jones representation of the braid group is also faithful for n = 4.
- culi
Interestingly, David Graeber argued that mathematical thinking likely began through initiatives of women. Specifically tied to practices like weaving, beadwork, and tracking plant-based knowledge.
https://theanarchistlibrary.org/library/david-graeber-and-da...
- wglb
Also https://www.yahoo.com/news/science/articles/99-old-mathemati.... Someone who has been at this problem for 60 years.
- marysminefnuf
Birman still dropping bangers at 100 is quite something. We knew 3 strands is faithful and it was assumed 4 must be true but the ramifications of this in the face of quantum computing will be really fun going forward.