Moduli spaces of convex projective structures on surfaces

2004/05/18 by Fock, V. V., Goncharov, A. B.
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0405348

Abstract

We define convex projective structures on 2D surfaces with holes and investigate their moduli space. We prove that this moduli space is canonically identified with the higher Teichmuller space for the group PSL₃ defined in our paper math/0311149. We define the quantum version of the moduli space of convex projective structures on surfaces with holes. The present paper can serve as an introduction to math/0311149. In the Appendix we show that the space of configurations of 5 flags in the projective plane is of cluster type E₇.

Related

• Moduli spaces of real projective structures on surfaces: Notes on a paper by V.V. Fock and A.B. Goncharov
• Description of moduli space of projective structures via fat graphs
• On Moduli Spaces of Convex Projective Structures on Surfaces: Outitude and Cell-Decomposition in Fock-Goncharov Coordinates
• Operads and moduli spaces
• Quantum geometry of moduli spaces of local systems and representation theory