Elsevier

Advances in Mathematics

Volume 208, Issue 1, 15 January 2007, Pages 249-273
Advances in Mathematics

Moduli spaces of convex projective structures on surfaces

To the memory of Yan Kogan
https://doi.org/10.1016/j.aim.2006.02.007Get rights and content
Under an Elsevier user license
open archive

Abstract

We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for SL3(R) defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version.

Keywords

Projective structures on surfaces
Teichmüller spaces
Cluster varieties

Cited by (0)