#### Volume 2, issue 1 (2002)

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A note on the Lawrence–Krammer–Bigelow representation

### Luisa Paoluzzi and Luis Paris

Algebraic & Geometric Topology 2 (2002) 499–518
 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 2000
Primary: 20F36
Secondary: 52C35, 52C30, 32S22