Higgs Bundles and Geometric Structures on Surfaces

Details Higgs Bundles and Geometric Structures on Surfaces Higgs Bundles and Geometric Structures on Surfaces

2008-05-12

arxiv.org/abs/0805.1793v1

The Many Facets of Geometry: a Tribute to Nigel Hitchin, Oxford University Press (2010), 129-163

Mathematics

Differential Geometry

29 pages, To appear in "The Many Facets of Geometry: a Tribute to Nigel Hitchin," Bourgignon, Garcia-Prada & Salamon, eds, Oxf

Scientific paper

This paper concerns the relationship between locally homogeneous geometric
structures on topological surfaces and the moduli of polystable Higgs bundles
on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the
uniformization of Riemann surfaces by hyperbolic geometry from this viewpoint,
and survey more recent developments in this theory.

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