Algebraic and Geometric Topology 2 (2002), paper no. 24, pages 499-518.

A note on the Lawrence-Krammer-Bigelow representation

Luisa Paoluzzi, Luis Paris

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

AMS subject classification. Primary: 20F36. Secondary: 52C35, 52C30, 32S22.

DOI: 10.2140/agt.2002.2.499

E-print: arXiv:math.GT/0111186

Submitted: 12 March 2002. (Revised: 5 June 2002.) Accepted: 5 June 2002. Published: 25 June 2002.

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Luisa Paoluzzi, Luis Paris
Laboratoire de Topologie, UMR 5584 du CNRS
Universite de Bourgogne, 9, avenue Alain Savary - BP 47870
21078 Dijon CEDEX - France
Email: paoluzzi@u-bourgogne.fr, lparis@u-bourgogne.fr

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