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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58766We 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.Symplectic Geometry53D30,53D50Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representationtext