Symplectic toric space associated to triangle inequalities (Q1851070)

The authors obtain a singular symplectic toric manifold with a convex polytope \(\Delta_n\) as the image of a moment map. \(\Delta_n\) is defined, using a symplectic structure on the moduli space of spatial polygons with \(n\) edges, \(M_n\), and a \(T^{n-3}\)-action on an open dense subset of \(M_n\). Moreover, for \(n=4,5,6,7,\) topological properties (Euler characteristic and virtual Poincaré polynomial) of this singular symplectic toric manifold are studied.