The Symplectic Geometry of Polygons in the 3-sphere
| dc.creator | Treloar, Thomas | |
| dc.date | 2000-09-20 | |
| dc.date.accessioned | 2026-07-07T04:37:38Z | |
| dc.date.available | 2026-07-07T04:37:38Z | |
| dc.description | We study the symplectic geometry of the moduli spaces $M_r=M_r(\s^3)$ 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 $C_r^n$, by the diagonal conjugation action of SU(2). Here $C_r^n$ is a quasi-Hamiltonian SU(2)-space. An integrable Hamiltonian system is constructed on $M_r$ in which the Hamiltonian flows are given by bending polygons along a maximal collection of nonintersecting diagonals. Finally, we show the symplectic structure on $M_r$ relates to the symplectic structure obtained from gauge-theoretic description of $M_r$. The results of this paper are analogues for the 3-sphere of results obtained for $M_r(\h^3)$, the moduli space of n-gons with fixed side-lengths in hyperbolic 3-space \cite{KMT}, and for $M_r(\E^3)$, the moduli space of n-gons with fixed side-lengths in $\E^3$ | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0009193 | |
| dc.identifier | http://arxiv.org/abs/math/0009193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59973 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D20;53D30 | |
| dc.title | The Symplectic Geometry of Polygons in the 3-sphere | |
| dc.type | text |