Braid Groups are Linear
Abstract
The braid groups B_n can be defined as the mapping class group of the npunctured disc. The LawrenceKrammer 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 npunctured 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:math/0005038
 Bibcode:
 2000math......5038B
 Keywords:

 Group Theory;
 Geometric Topology;
 20F36 (Primary) 57M07;
 20C15 (Secondary)
 EPrint:
 13 pages, 3 figures