ArXiv.org · 1996 · 32 citations · 3 references
Natural SciencesMathematicsDescriptive GeometryGeometryTopologyAlgebraic GeometryDifferential GeometryEuclidean GeometryProjective GeometrySymplectic GeometryBendingEquivariant TopologyPolygon GeometryPolygon TheorySymplectic Field TheorySymplectic MapsSymplectic ReductionSymplectic Spaces
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.
3