arXiv Analytics

Sign in

arXiv:math/0005038 [math.GR]AbstractReferencesReviewsResources

Braid Groups are Linear

Stephen J. Bigelow

Published 2000-05-04Version 1

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.

Comments: 13 pages, 3 figures
Categories: math.GR, math.GT
Subjects: 20F36, 57M07, 20C15
Related articles: Most relevant | Search more
arXiv:1106.4165 [math.GR] (Published 2011-06-21, updated 2012-02-13)
Zariski density and finite quotients of mapping class groups
arXiv:math/0603397 [math.GR] (Published 2006-03-16)
Braid Group of a Genetic Code
arXiv:0904.1469 [math.GR] (Published 2009-04-09)
Presentations of subgroups of the braid group generated by powers of band generators

Links

Toolbox