Cohomology of SL2,C character varieties of surface groups and the action of the Torelli group - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: We determine the action of the Torelli group on the equivariant cohomology ofthe space of flat SL2,C connections on a closed Riemann surface. We show thatthe trivial part of the action contains the equivariant cohomology of the evencomponent of the space of flat PSL2,C connections. The non-trivial partconsists of the even alternating products of degree two Prym representations,so that the kernel of the action is precisely the Prym-Torelli group. Wecompute the Betti numbers of the ordinary cohomology of the moduli space offlat SL2,C connections. Using results of Cappell-Lee-Miller we show that thePrym-Torelli group, which acts trivially on equivariant cohomology, actsnon-trivially on ordinary cohomology.



Author: Georgios D. Daskalopoulos, Richard A. Wentworth, Graeme Wilkin

Source: https://arxiv.org/



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