MULTIVARIABLE BURAU MATRICES AND LABELED LINE CONFIGURATIONS

We study labeled configurations of la pairwise disjoint lines in proje ctive 3-space, up to ''rigid isotopy''. To this end, we introduce the ''Labeled Braid Group'', and give a linear representation for it, whic h can be regarded as a labeled version of the Burau representation. We give a topological path model for these multi-variable matrices, and use them to compute the Gassner matrix of a pure braid and the Alexand er polynomial of the link associated with a labeled line configuration .