Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 035, 30 pages      arXiv:1809.05747      https://doi.org/10.3842/SIGMA.2019.035
Contribution to the Special Issue on Geometry and Physics of Hitchin Systems

An Introduction to Higgs Bundles via Harmonic Maps

Qiongling Li
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China

Received October 16, 2018, in final form April 26, 2019; Published online May 04, 2019

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.

Key words: Higgs bundles; harmonic maps; non-abelian Hodge correspondence.

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