Cross ratios and identities for higher Teichmüller-Thurston theory
Labourie, François ; McShane, Gregory
Duke Math. J., Tome 146 (2009) no. 1, p. 279-345 / Harvested from Project Euclid
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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 ${\rm{PSL}}(n,\mathbb R)$ . 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
Publié le : 2009-08-15
Classification:  32G15,  32G07 
@article{1248182808,
     author = {Labourie, Fran\c cois and McShane, Gregory},
     title = {Cross ratios and identities for higher Teichm\"uller-Thurston theory},
     journal = {Duke Math. J.},
     volume = {146},
     number = {1},
     year = {2009},
     pages = { 279-345},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1248182808}
}

Labourie, François; McShane, Gregory. Cross ratios and identities for higher Teichmüller-Thurston theory. Duke Math. J., Tome 146 (2009) no. 1, pp.  279-345. http://gdmltest.u-ga.fr/item/1248182808/