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The Many Facets of GeometryA Tribute to Nigel Hitchin$
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Oscar Garcia-Prada, Jean Pierre Bourguignon, and Simon Salamon

Print publication date: 2010

Print ISBN-13: 9780199534920

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199534920.001.0001

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Higgs Bundles and Geometric Structures on Surfaces

Higgs Bundles and Geometric Structures on Surfaces

(p.129) VIII Higgs Bundles and Geometric Structures on Surfaces
The Many Facets of Geometry

William M. Goldman

Oxford University Press

The theory of Higgs bundles, pioneered by Hitchin and Simpson, provides an analytic approach to studying surface group representations and their deformation space. This chapter describes the basic examples of this theory, emphasizing relations to deformation and rigidity of geometric structures. In particular, it reports on some very recent developments when G is a real Lie group, either a split real semisimple group or an automorphism group of a Hermitian symmetric space of noncompact type.

Keywords:   Higgs bundles, geometric structures, Lie group, Simpson, deformation, rigidity

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