Moduli spaces of convex projective structures on surfaces

By V. Fock, A. Goncharov. 2004

86 citations recorded by the source corpus.

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 Teichmuller space for SL 3 ( R ) defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmuller theory, math.AG/0311149 ]. We investigate the cluster structure of this moduli space, and define its quantum version.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1b22e7194e02c3293d7058e222f765d2005e29fd

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Polynomial cubic differentials and convex polygons in the projective plane (2014, unknown): “(Compare the “toy model” of the space of convex projective structures described in [FG07].”
Surface group representations with maximal Toledo invariant (2003, background): “The problem of understanding the representation variety Hom 1() ;G of the fundamental group 1() of into G has received considerable interest [34, 33, 42, 35, 61, 41, 6, 48, 49, 28, 27 ]; in particular the search for special connected components of the representation variety and their geometric sign”
The Pentagram Map: A Discrete Integrable System (2008, background): “On the one hand, the space of twisted polygons is known as an example of cluster manifold, see [6,7] and discussion in the end of this paper.”
Around groups in Hilbert Geometry (2013, background): “The situation of SL3(R) is much simpler than the situation of a general semisimple Lie group, and there is a specific article dealing with Fock-Goncharov coordinates in the context of β(Σ), that the reader will be happy to read: [37].”
Tensor diagrams and cluster algebras (2012, unknown): “Goncharov [10] on PGL3-Teichmüller spaces.”
2-frieze patterns and the cluster structure of the space of polygons (2010, background): “In [10, 11] (see also [21], Section 6.”