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: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| 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| _version_ | 1862619747535814656 |
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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 |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210187 |
| 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. en 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 |
| work_keys_str_mv | AT liq anintroductiontohiggsbundlesviaharmonicmaps AT liq introductiontohiggsbundlesviaharmonicmaps |