  The braid groups B_n can be defined as the mapping class group of the
n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is
the induced action on a certain twisted second homology of the space of
unordered pairs of points in the n-punctured disc. Recently, Daan Krammer
showed that this is a faithful representation in the case n=4. In this paper,
we show that it is faithful for all n.
