2000/09/20 by Thomas Treloar, Treloar, Thomas
Computer Science · Mathematics · Physics and Astronomy · #53D20 #53D30 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Mathematics and Applications #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG #msc:53D20 #msc:53D30
paper · pdf · doi:10.48550/arxiv.math/0009193
23 pages
arxiv created 2000/09/20 · openalex publication_date 2000/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the symplectic geometry of the moduli spaces Mr=Mr(\s3) of closed n-gons with fixed side-lengths in the 3-sphere. We prove that these moduli spaces have symplectic structures obtained by reduction of the fusion product of n conjugacy classes in SU(2), denoted Crn, by the diagonal conjugation action of SU(2). Here Crn is a quasi-Hamiltonian SU(2)-space. An integrable Hamiltonian system is constructed on Mr in which the Hamiltonian flows are given by bending polygons along a maximal collection of nonintersecting diagonals. Finally, we show the symplectic structure on Mr relates to the symplectic structure obtained from gauge-theoretic description of Mr. The results of this paper are analogues for the 3-sphere of results obtained for Mr(\h3), the moduli space of n-gons with fixed side-lengths in hyperbolic 3-space \citeKMT, and for Mr(\E3), the moduli space of n-gons with fixed side-lengths in \E3