Algebraic & Geometric Topology 2 (2002) 499–518

DOI: 10.2140/agt.2002.2.499

arXiv: math.GT/0111186

Abstract

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.

Keywords

braid groups, linear representations, Salvetti complexes

Mathematical Subject Classification

Primary: 20F36

Secondary: 32S22, 52C30, 52C35

References

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Publication

Received: 12 March 2002
Revised: 5 June 2002
Accepted: 5 June 2002
Published: 25 June 2002

Authors