Higgs bundles and diffeomorphism groups

TL;DR

This paper explores the extension of Higgs bundle equations to symplectic diffeomorphism groups, introducing the concept of folded hyperkähler 4-manifolds and conjecturing a new family of metrics parametrized by an infinite-dimensional space.

Contribution

It introduces the notion of folded hyperkähler 4-manifolds and conjectures a new family of metrics related to Higgs bundles and symplectic diffeomorphisms.

Findings

Introduction of folded hyperkähler 4-manifolds

Conjecture of a family of metrics parametrized by an infinite-dimensional space

Connection between Higgs bundles and symplectic diffeomorphism groups

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 hyperkaehler 4-manifold and conjecture the existence of a family of such metrics parametrised by an infinite-dimensional analogue of Teichmueller space.