Harmonic Maps and Hypersymplectic Geometry

Harmonic Maps and Hypersymplectic Geometry

We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a \(G\)-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this moduli space is globally not well-behaved. Howeve...

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1. Verfasser: Röser, Markus
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Geometry
Linear algebra
Mathematics - Differential Geometry
Mathematics - Symplectic Geometry
Topological manifolds
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description We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a \(G\)-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this moduli space is globally not well-behaved. However, we are able to construct a smooth open set consisting of solutions with small Higgs field, on which we can investigate the hypersymplectic geometry. Finally, we reinterpret our results in terms of the Riemannian geometry of the moduli space of \(G\)-connections.
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subjects Geometry
Linear algebra
Mathematics - Differential Geometry
Mathematics - Symplectic Geometry
Topological manifolds
title Harmonic Maps and Hypersymplectic Geometry
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