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

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

2000-02-25

arxiv.org/abs/math/0002222v1

Mathematics

Symplectic Geometry

Scientific paper

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.

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