Cross Ratios and Identities for Higher Thurston Theory

Abstract

We generalise in this article the Mc Shane-Mirzakhani identities in hyperbolic geometry to arbitrary cross ratios. We give an expression of them in the case of Hitchin representations of surface groups in PSL(n, R) in a suitable choice of Fock-Goncharov coordinates.

64 pages, 5 figures The new version corrects many typos, sign errors and imprecisions. The writing has been hopefully improved. The mathematical content is identical

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• Cross Ratios and Identities for Higher Thurston Theory

Cited by in corpus (17)

• Cross Ratios and Identities for Higher Thurston Theory
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• Degeneration of Hitchin representations along internal sequences
• Collar lemma for Hitchin representations
• Higher spin JT gravity and a matrix model dual
• Positive surface group representations in PO(p,q)
• Noncommutative Cross-Ratios
• Basmajian's identity in higher Teichmüller-Thurston theory
• Surface groups in uniform lattices of some semi-simple groups
• Geodesic and orthogeodesic identities on hyperbolic surfaces
• Volume of the moduli space of unmarked bounded positive convex ${\mathbb{RP}}^2$ structures
• On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces
• Primitive stable representations in higher rank semisimple Lie groups
• McShane's Identity in Rank One Symmetric Spaces
• The probabilistic nature of McShane's identity: planar tree coding of simple loops
• Infinitesimal Liouville currents, cross-ratios and intersection numbers