Surveys in Differential Geometry

Volume 21 (2016)

Higgs bundles and diffeomorphism groups

Pages: 139 – 163

DOI: https://dx.doi.org/10.4310/SDG.2016.v21.n1.a4

Author

Nigel Hitchin (Mathematical Institute, University of Oxford, United Kingdom)

Abstract

By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere, we encounter the notion of a folded hyperkähler 4-manifold and conjecture the existence of a family of such metrics parametrised by an infinite-dimensional analogue of Teichmüller space.

Keywords

hyperkähler, Teichmüller space, Higgs bundle, Toda equation

2010 Mathematics Subject Classification

53C26

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Published 13 January 2022