Duke Mathematical Journal

Cross ratios and identities for higher Teichmüller-Thurston theory

François Labourie and Gregory McShane

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Abstract

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

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

Dates
First available in Project Euclid: 21 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1248182808

Digital Object Identifier
doi:10.1215/00127094-2009-040

Mathematical Reviews number (MathSciNet)
MR2541705

Zentralblatt MATH identifier
1182.30075

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

Citation

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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