Quantization of bending deformations of polygons in Euclidean space,   hypergeometric integrals and the Gassner representation
  We quantize the bending deformations of n-gon linkages by linearizing the bending fields at a degenerate n-gon to get a representation of the Malcev Lie algebra of the pure braid group. This linearization yields a flat connection on the space of n distinct points on the complex line. We show that the monodromy is (essentially) the Gassner representation. 
Michael Kapovich and John J. Millson