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arXiv · 1102.4175

Higgs bundles and the real symplectic group

Peter B. Gothen
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Abstract

We give an overview of the work of Corlette, Donaldson, Hitchin and Simpson leading to the non-abelian Hodge theory correspondence between representations of the fundamental group of a surface and the moduli space of Higgs bundles. We then explain how this can be generalized to a correspondence between character varieties for representations of surface groups in real Lie groups G and the moduli space of G-Higgs bundles. Finally we survey recent joint work with Bradlow, García-Prada and Mundet i Riera on the moduli space of maximal Sp(2n,R)-Higgs bundles.

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Peter B. Gothen. 2011-03-06. Higgs bundles and the real symplectic group. https://doi.org/10.1063/1.3599126

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