Piecewise circular curves and Positivity
Abstract
We introduce the moduli space of generic circular n -gons in the Riemann sphere and relate it to a moduli space of Legendrian polygons. We prove that when n = 2 k , this moduli space contains a connected component homeomorphic to the Fock–Goncharov space of k -tuples of positive flags for PSp ( 4 , ℝ ) and hence is a topological ball. We characterize this component geometrically as the space of simple circular n -gons with decreasing curvature.
Fields of Study & Subjects
Geometric and Algebraic Topology
Algebraic Geometry and Number Theory
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Annales de l’institut Fourier
- Pages
- 1–44
- Publication date
- 26 March 2026
- Language
- EN