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Cross ratios and identities for higher Teichmüller-Thurston theory. (English) Zbl 1182.30075

The paper gives certain generalisations of “McShane-Mirzakhani identities in hyperbolic geometry” to arbitrary cross ratios, and of “Hitchin representations of open surface groups” to \(PSL_n({\mathbb R})\). The idea is to associate cross ratios to these representations, and then to elaborate explicit formulae for the generalised identities.

MSC:

30F60 Teichmüller theory for Riemann surfaces
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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