Moduli Spaces of Polygons and Punctured Riemann Spheres

Abstract

AbstractThe purpose of this note is to give a simple combinatorial construction of the map from the canonically compactified moduli spaces of punctured complex projective lines to the moduli spaces 𝓟r of polygons with fixed side lengths in the Euclidean space 𝔼3. The advantage of this construction is that one can obtain a complete set of linear relations among the cycles that generate homology of 𝓟r. We also classify moduli spaces of pentagons.