Hitchin components and hyperconvex representations of surface groups. (Composantes de Hitchin et représentations hyperconvexes de groupes de surface.) (French) Zbl 1223.57015

Guichard, Olivier

J. Differ. Geom. 80, No. 3, 391-431 (2008).

Summary: We show that the notion of hyperconvex representation due to F. Labourie [Invent. Math. 165, No. 1, 51–114 (2006; Zbl 1103.32007)] gives a geometric characterization of the representations of a surface group in \(\text{PSL}_n(\mathbb R)\) that belong to the Hitchin component.

MSC:

57M50	General geometric structures on low-dimensional manifolds
32G15	Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
20C99	Representation theory of groups
30F60	Teichmüller theory for Riemann surfaces

Citations:

Zbl 1103.32007