Cohomology of $SL(2,C)$ Character Varieties of Surface Groups and the Action of the Torelli Group
Daskalopoulos, Georgios D. ; Wentworth, Richard A. ; Wilkin, Graeme
Asian J. Math., Tome 14 (2010) no. 1, p. 359-384 / Harvested from Project Euclid
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We determine the action of the Torelli group on the equivariant cohomology of the space of flat $SL(2, C)$ connections on a closed Riemann surface. We show that the trivial part of the action contains the equivariant cohomology of the even component of the space of flat $PSL(2, C)$ connections. The non-trivial part consists of the even alternating products of degree two Prym representations, so that the kernel of the action is precisely the Prym-Torelli group. We compute the Betti numbers of the ordinary cohomology of the moduli space of flat $SL(2, C)$ connections. Using results of Cappell-Lee-Miller we show that the Prym-Torelli group, which acts trivially on equivariant cohomology, acts non-trivially on ordinary cohomology.
Publié le : 2010-09-15
Classification:  Character varieties,  Higgs bundles,  Torelli group,  57M50,  58E20,  53C24 
@article{1295040755,
     author = {Daskalopoulos, Georgios D. and Wentworth, Richard A. and Wilkin, Graeme},
     title = {Cohomology of $SL(2,C)$ Character Varieties of Surface Groups and the Action of the Torelli Group},
     journal = {Asian J. Math.},
     volume = {14},
     number = {1},
     year = {2010},
     pages = { 359-384},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1295040755}
}

Daskalopoulos, Georgios D.; Wentworth, Richard A.; Wilkin, Graeme. Cohomology of $SL(2,C)$ Character Varieties of Surface Groups and the Action of the Torelli Group. Asian J. Math., Tome 14 (2010) no. 1, pp.  359-384. http://gdmltest.u-ga.fr/item/1295040755/