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Cross ratios, surface groups, P S L ( n , 𝐑 ) and diffeomorphisms of the circle

François Labourie (2007)

Publications Mathématiques de l'IHÉS

This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into C 1 , h ( 𝕋 ) Diff h ( 𝕋 ) associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...

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