An Introduction to Higgs Bundles via Harmonic Maps

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...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Author: Li, Q.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210187
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:An Introduction to Higgs Bundles via Harmonic Maps / Q. Li // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 57 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Li, Q.
author_facet Li, Q.
citation_txt An Introduction to Higgs Bundles via Harmonic Maps / Q. Li // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 57 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2025-12-07T21:24:41Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T21:24:41Z
publishDate 2019
publisher Інститут математики НАН України
record_format dspace
spelling Li, Q.
2025-12-03T14:30:50Z
2019
An Introduction to Higgs Bundles via Harmonic Maps / Q. Li // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 57 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53C43; 53C07; 53C21
arXiv: 1809.05747
https://nasplib.isofts.kiev.ua/handle/123456789/210187
https://doi.org/10.3842/SIGMA.2019.035
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.
The author would like to thank the anonymous referees for numerous suggestions and comments to help improve the manuscript. The author also thanks Laura Schaposnik for her kind invitation to give the mini-course in the RTG workshop in June 2018 at UIC, and both her and Lara Anderson for the encouragement to write these notes. The author acknowledges support from UIC NSF RTG Grant DMS-1246844, the UIC Start-Up Fund of Laura Schaposnik, and the grants NSF DMS 107452, 1107263, 1107367 RNMS: GEometric structures And Representation varieties (the GEAR Network). The author acknowledges support from the Nankai Zhide Foundation.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
An Introduction to Higgs Bundles via Harmonic Maps
Article
published earlier
spellingShingle An Introduction to Higgs Bundles via Harmonic Maps
Li, Q.
title An Introduction to Higgs Bundles via Harmonic Maps
title_full An Introduction to Higgs Bundles via Harmonic Maps
title_fullStr An Introduction to Higgs Bundles via Harmonic Maps
title_full_unstemmed An Introduction to Higgs Bundles via Harmonic Maps
title_short An Introduction to Higgs Bundles via Harmonic Maps
title_sort introduction to higgs bundles via harmonic maps
url https://nasplib.isofts.kiev.ua/handle/123456789/210187
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