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

Researchers Bharathram, Birman, and Brendle proved that the Burau representation of the braid group is faithful for n=4, resolving a longstanding question in geometric topology. This result immediately implies that the Jones representation of the braid group is also faithful for n=4, and builds on earlier work by Moody, Long, and Bigelow.