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Representations of surface groups and Higgs bundles - I

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Moduli Spaces

Classical Hodge theory uses harmonic forms as preferred representatives of cohomology classes. A representation of the fundamental group of a Riemann surface gives rise to a corresponding flat bundle. A Theorem of Donaldson and Corlette shows how to find a harmonic metric in this bundle. A flat bundle corresponds to class in first non-abelian cohomology and the Theorem can be viewed as an analogue of the classical representation of de Rham cohomology classes by harmonic forms.

This talk is part of the Isaac Newton Institute Seminar Series series.

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