6533b7defe1ef96bd1275d1d

RESEARCH PRODUCT

A note on the Lawrence-Krammer-Bigelow representation

Luisa PaoluzziLuis Paris

subject

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsLinear representation[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)52C3001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]52C35Mathematics - Geometric TopologyMathematics::Group TheoryMathematics::Algebraic Geometry[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics20F36 52C35 52C30 32S22braid groups0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]linear representations010102 general mathematicsRepresentation (systemics)FibrationSalvetti complexesGeometric Topology (math.GT)Mathematics::Geometric TopologyHyperplaneMonodromy010307 mathematical physicsGeometry and TopologyMathematics - Group Theory32S22

description

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.

yearjournalcountryeditionlanguage
2002-06-25
https://hal.archives-ouvertes.fr/hal-01275380