• Corpus ID: 237213320

Piecewise circular curves and positivity

  title={Piecewise circular curves and positivity},
  author={Jean-Philippe Burelle and Ryan Kirk},
We introduce the moduli space of generic piecewise circular n-gons in the Riemann sphere and relate it to a moduli space of Legendrian polygons. We prove that when n = 2k, 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 piecewise circular curves with decreasing curvature. 

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