TY - JOUR
T1 - Cohomology of SL(2,C) Character Varieties of Surface Groups and the Action of the Torelli Group
AU - Daskalopoulos, Georgios
AU - Wentworth, Richard
AU - Wilkin, Graeme Peter Desmond
PY - 2010/1/1
Y1 - 2010/1/1
N2 - 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.
AB - 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.
U2 - 10.4310/AJM.2010.v14.n3.a5
DO - 10.4310/AJM.2010.v14.n3.a5
M3 - Article
VL - 14
SP - 359
EP - 384
JO - Asian Journal of Mathematics
JF - Asian Journal of Mathematics
SN - 1093-6106
IS - 3
ER -