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math.SG2000
Quantization of bending deformations of polygons in Euclidean space, hypergeometric integrals and the Gassner representation
Michael Kapovich, John J. Millson
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 g…
math.SG1999
The symplectic geometry of polygons in hyperbolic 3-space
Michael Kapovich, John J. Millson, Thomas Treloar
We study the symplectic geometry of the moduli space of closed n-gons with fixed side-lengths in hyperbolic 3-space. We prove that these moduli spaces have a symplectic structure c…