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
Buraurepresentation 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.
Keywords
Burau representation, braid group, free group, Heisenberg
group, Klein 4-group
