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

Michael Kapovich·John J. Millson
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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.

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Michael Kapovich, John J. Millson. 2000-02-25. Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation. https://arxiv.org/abs/math/0002222

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