Higgs Bundles and Geometric Structures on Surfaces

William M. Goldman

Type: Book-Chapter

Publication Date: 2010-07-01

Citations: 9

DOI: https://doi.org/10.1093/acprof:oso/9780199534920.003.0008

Abstract

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.

Locations

arXiv (Cornell University) - View - PDF
Oxford University Press eBooks - View

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