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MOS

Seminar

Representations of surface groups and Higgs bundles - II

Gothen, P (Universidade do Porto)
Monday 10 January 2011, 11:30-12:30

Meeting Room 2, CMS

Abstract

A Higgs bundle on a Riemann surface is a pair consisting of a holomorphic bundle and a holomorphic one-form, the Higgs field, with values in a certain associated vector bundle. A theorem of Hitchin and Simpson says that a stable Higgs bundle admits a metric satisfying Hitchin's equations. Together with the Theorem of Corlette and Donaldson, the Hitchin-Kobayashi correspondence generalizes the classical Hodge decomposition of the first cohomology of the Riemann surface, providing a correspondence between isomorphism classes of Higgs bundles and representations of the fundamental group of the surface.

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