Faithful linear representations of the braid groups. (English) Zbl 1050.20026

Turaev, Vladimir

Séminaire Bourbaki. Volume 1999/2000. Exposés 865–879. Paris: Société Mathématique de France. Astérisque 276, 389-409, Exp. No. 878 (2002).

This is a survey of recent work of D. Krammer [Ann. Math. (2) 155, No. 1, 131–156 (2002; Zbl 1020.20025), S. J. Bigelow [J. Am. Math. Soc. 14, No. 2, 471–486 (2001; Zbl 0988.20021)] and M. G. Zinno [Math. Ann. 321, No. 1, 197–211 (2001; Zbl 1042.20023)] on the non-faithfulness of the Burau representation of the braid groups, and of the faithfulness of Krammer’s representation.
For the entire collection see [Zbl 0981.00011].

Reviewer: Carl Droms (Harrisonburg)

MSC:

20F36	Braid groups; Artin groups
57Q45	Knots and links in high dimensions (PL-topology) (MSC2010)

Keywords:

braid groups; Burau representation; Krammer representation

Citations:

Zbl 1042.20023; Zbl 1020.20025; Zbl 0988.20021