English

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}
}