Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation

Kapovich, Michael; Millson, John J.

Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation

Authors

Description

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.