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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 Bn. 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
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Publication
Received: 12 March 2002
Revised: 5 June 2002
Accepted: 5 June 2002
Published: 25 June 2002
Authors
Luisa Paoluzzi
Laboratoire de Topologie
UMR 5584 du CNRS
Université de Bourgogne
9, avenue Alain Savary
BP 47870
21078 Dijon CEDEX
France
Luis Paris
Laboratoire de Topologie
UMR 5584 du CNRS
Université de Bourgogne
9, avenue Alain Savary
BP 47870
21078 Dijon CEDEX
France