Geodesic
A note on the Lawrence–Krammer–Bigelow representation
Paoluzzi, Luisa1 ; Paris, Luis1
1Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, 9, avenue Alain Savary, BP 47870, 21078 Dijon CEDEX, France
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 499-518
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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.

DOI : 10.2140/agt.2002.2.499
Keywords: braid groups, linear representations, Salvetti complexes

Paoluzzi, Luisa  1   ; Paris, Luis  1

1 Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, 9, avenue Alain Savary, BP 47870, 21078 Dijon CEDEX, France 
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Paoluzzi, Luisa; Paris, Luis. A note on the Lawrence–Krammer–Bigelow representation. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 499-518. doi: 10.2140/agt.2002.2.499

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