Braid groups are linear

The braid group B n B_n can be defined as the mapping class group of the n n -punctured disk. A group is said to be linear if it admits a faithful representation into a group of matrices over R \mathbf R . Recently Daan Krammer has shown that a certain representation of the braid groups is faithful for the case n = 4 n=4 . In this paper, we show that it is faithful for all n n .