A symplectic map between hyperbolic and complex Teichmüller theory
Krasnov, Kirill ; Schlenker, Jean-Marc
Duke Math. J., Tome 146 (2009) no. 1, p. 331-356 / Harvested from Project Euclid
Let $S$ be a closed, orientable surface of genus at least $2$ . The space ${\mathcal T}_H\times {\mathcal ML}$ , where ${\mathcal T}_H$ is the “hyperbolic” Teichmüller space of $S$ and ${\mathcal ML}$ is the space of measured geodesic laminations on $S$ , is naturally a real symplectic manifold. The space ${\mathcal CP}$ of complex projective structures on $S$ is a complex symplectic manifold. A relation between these spaces is provided by Thurston's grafting map ${\rm Gr}$ . We prove that this map, although not smooth, is symplectic. The proof uses a variant of the renormalized volume defined for hyperbolic ends
Publié le : 2009-11-01
Classification:  30F60,  32G15
@article{1255699343,
     author = {Krasnov, Kirill and Schlenker, Jean-Marc},
     title = {A symplectic map between hyperbolic and complex Teichm\"uller theory},
     journal = {Duke Math. J.},
     volume = {146},
     number = {1},
     year = {2009},
     pages = { 331-356},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255699343}
}
Krasnov, Kirill; Schlenker, Jean-Marc. A symplectic map between hyperbolic and complex Teichmüller theory. Duke Math. J., Tome 146 (2009) no. 1, pp.  331-356. http://gdmltest.u-ga.fr/item/1255699343/