Surveys in Differential Geometry
Volume 21 (2016)
Higgs bundles and diffeomorphism groups
Pages: 139 – 163
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.
hyperkähler, Teichmüller space, Higgs bundle, Toda equation
2010 Mathematics Subject Classification