Polygon spaces and Grassmannians

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

Differential Geometry

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/152113

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9602012
 http://arxiv.org/abs/dg-ga/9602012

Collections

arXiv