In 1936 W. Burau discovered an interesting family of matrices that give a linear representation of Artin’s classical braid group , . A natural question followed very quickly: is the so-called Burau representation faithful? Over the years it was proved to be faithful for , nonfaithful for , but the case of remains open to this day, in spite of many papers on the topic. This paper introduces braid groups, describes the problem in ways that make it accessible to readers with a minimal background, reviews the literature, and makes a contribution that reinforces conjectures that the Burau representation of is faithful.
"On the Burau representation of $B_4$." Involve 14 (1) 143 - 154, 2021. https://doi.org/10.2140/involve.2021.14.143