Finite and infinite representations of surface groups and cross ratios

Finite and infinite representations of surface groups and cross ratios

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Francois Labourie, Universite de Paris-Sud
Fine Hall 314

In this talk, I explain how cross ratios—special functions of four arguments—on the boundary at infinity of surfaces groups describe both finite (in SL(nR)) and infinite (in a group related to diffeomorphisms of the circle) dimensional representations of surface groups. If time permits, I will explain what are the generalisation of McShane's identity in that context as well as some conjectural picture relating these representations to complex analysis.