Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation
Symplectic Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0002222,
title = {Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation},
author = {Michael Kapovich and John J. Millson},
journal= {arXiv preprint arXiv:math/0002222},
year = {2007}
}