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Braid groups are linear. (English) Zbl 0988.20021

D. Krammer [Invent. Math. 142, No. 3, 451-486 (2000; see the review Zbl 0988.20023 below)] proved that a representation of the braid groups B n is faithful in the case n=4. The representation Krammer used is essentially the same as one used by R. J. Lawrence [Commun. Math. Phys. 135, No. 1, 141-191 (1990; Zbl 0716.20022)]. The author calls this representation the Lawrence-Krammer representation.

In the paper the author proves by topological methods that the Lawrence-Krammer representation is faithful for all n.


MSC:
20F36Braid groups; Artin groups
20C15Ordinary representations and characters of groups
57M07Topological methods in group theory