The Hodge theory of character varieties
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Publication:2918456
zbMATH Open1254.14009arXiv1011.0784MaRDI QIDQ2918456
Publication date: 6 October 2012
Abstract: This is a report on joint work with T. Hausel and L. Migliorini, where we prove, for each of the groups GL(2,C), PGL(2,C), SL(2,C), that the non-Abelian Hodge theorem identifies the weight filtration on the cohomology of the character variety with the perverse Leray filtration on the cohomology of the domain of the Hitchin map. We review the decomposition theorem, N^go's support theorem, the geometric description of the perverse filtration and the sub-additivity of the Leray filtration with respect to the cup product.
Full work available at URL: https://arxiv.org/abs/1011.0784
Related Items (7)
Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams ⋮ Topology of Hitchin systems and Hodge theory of character varieties: the case \(A_1\) ⋮ Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ The Hodge-FVH correspondence ⋮ A note on the characteristic p nonabelian Hodge theory in the geometric case ⋮ Representations of fundamental groups whose Higgs bundles are pullbacks
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