Duke Mathematical Journal

Cross ratios and identities for higher Teichmüller-Thurston theory

François Labourie and Gregory McShane

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We generalise the McShane-Mirzakhani identities from hyperbolic geometry to arbitrary cross ratios. We define and study Hitchin representations of open surface groups to PSL(n,R). We associate cross ratios to these representations and then give explicit expressions for our generalised identities in terms of (a suitable choice of) Fock-Goncharov coordinates

Article information

Duke Math. J., Volume 149, Number 2 (2009), 279-345.

First available in Project Euclid: 21 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
Secondary: 32G07: Deformations of special (e.g. CR) structures


Labourie, François; McShane, Gregory. Cross ratios and identities for higher Teichmüller-Thurston theory. Duke Math. J. 149 (2009), no. 2, 279--345. doi:10.1215/00127094-2009-040. https://projecteuclid.org/euclid.dmj/1248182808

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