An Introduction to Higgs Bundles via Harmonic Maps

Abstract

This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence. With the preparation, we review current progress towards some open problems in the study of equivariant harmonic maps.

References in corpus (12)

• The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations
• Ends of the moduli space of Higgs bundles
• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
• Deformations of maximal representations in Sp(4,R)
• G2 geometry and integrable systems
• Asymptotics of certain families of Higgs bundles in the Hitchin component
• Cyclic Higgs bundles and the affine Toda equations
• Survey on Affine Spheres
• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Generic Ends of the Moduli Space of $SL(n,\mathbb{C})$-Higgs Bundles
• Polynomial cubic differentials and convex polygons in the projective plane

Cited by in corpus (9)

• Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces
• Non-Abelian Hodge Theory and Related Topics
• Domination results in $n$-Fuchsian fibers in the moduli space of Higgs bundles
• Nilpotent Higgs bundles and the Hodge metric on the Calabi-Yau moduli
• Studying Deformations of Fuchsian Representations with Higgs Bundles
• Complete solutions of Toda equations and cyclic Higgs bundles over non-compact surfaces
• Length spectrum compactification of the ${\mathrm{SO}}_0(2,3)$-Hitchin component
• Harmonic maps from Kähler manifolds
• The conformal limit and projective structures