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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

Chapter:
(p.129) VIII Higgs Bundles and Geometric Structures on Surfaces
Source:
The Many Facets of Geometry
Author(s):

William M. Goldman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199534920.003.0008

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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