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Polygon spaces and Grassmannians

Jean-Claude Hausmann·Allen Knutson
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Abstract

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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BibTeXRIS

Jean-Claude Hausmann, Allen Knutson. 1996-02-29. Polygon spaces and Grassmannians. https://arxiv.org/abs/dg-ga/9602012

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