Moduli spaces of convex projective structures on surfaces

Details Moduli spaces of convex projective structures on surfaces Moduli spaces of convex projective structures on surfaces

2004-05-18

arxiv.org/abs/math/0405348v2

Mathematics

Differential Geometry

Final version, to appear in Advances in Math. The appendix is new

Scientific paper

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 PSL_3 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 E_7.

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