Abstract
In 1936 W. Burau discovered an interesting family of n×n matrices that give a linear representation of Artin’s classical braid group Bn, n=1,2,…. A natural question followed very quickly: is the so-called Burau representation faithful? Over the years it was proved to be faithful for n≤3, nonfaithful for n≥5, but the case of n=4 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 B4 is faithful.
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