2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59119The 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.13 pages, 3 figuresGroup TheoryGeometric Topology20F36 (Primary) 57M07, 20C15 (Secondary)text