Polygon spaces and Grassmannians

Details Polygon spaces and Grassmannians Polygon spaces and Grassmannians

1996-02-29

arxiv.org/abs/dg-ga/9602012v1

Mathematics

Differential Geometry

plain TeX, 21 pages, submitted to Journal of Differential Geometry

Scientific paper

We study the moduli spaces of polygons in R^2 and R^3, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gel'fand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson arise as a reduction of the Gel'fand-Cetlin system on the Grassmannian, and with these determine the pentagon and hexagon spaces up to equivariant symplectomorphism. Other than invocation of Delzant's theorem, our proofs are purely polygon-theoretic in nature.

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