Higgs Bundles and Geometric Structures on Manifolds
Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people, and they play an important role in higher Teichmüller theory. Geometric structures on a manifold are closely related to representations of the fund...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210183 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Higgs Bundles and Geometric Structures on Manifolds / D. Alessandrini // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 42 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712268873007104 |
|---|---|
| author | Alessandrini, D. |
| author_facet | Alessandrini, D. |
| citation_txt | Higgs Bundles and Geometric Structures on Manifolds / D. Alessandrini // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 42 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people, and they play an important role in higher Teichmüller theory. Geometric structures on a manifold are closely related to representations of the fundamental group and flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchin's equations. Baraglia has shown in his Ph.D. The thesis is that Higgs bundles can also be used to construct geometric structures in some interesting cases. In this paper, we will explain the main ideas behind this theory, and we will survey some recent results in this direction, which are joint work with Qiongling Li.
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| first_indexed | 2025-12-07T21:24:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210183 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:40Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Alessandrini, D. 2025-12-03T14:28:26Z 2019 Higgs Bundles and Geometric Structures on Manifolds / D. Alessandrini // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 42 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57M50; 53C07; 22E40 arXiv: 1809.07290 https://nasplib.isofts.kiev.ua/handle/123456789/210183 https://doi.org/10.3842/SIGMA.2019.039 Geometric structures on manifolds became popular when Thurston used them in his work on the geometrization conjecture. They were studied by many people, and they play an important role in higher Teichmüller theory. Geometric structures on a manifold are closely related to representations of the fundamental group and flat bundles. Higgs bundles can be very useful in describing flat bundles explicitly, via solutions of Hitchin's equations. Baraglia has shown in his Ph.D. The thesis is that Higgs bundles can also be used to construct geometric structures in some interesting cases. In this paper, we will explain the main ideas behind this theory, and we will survey some recent results in this direction, which are joint work with Qiongling Li. I am grateful to Qiongling Li for the collaboration that brought many of the results surveyed here, to Steve Bradlow, Brian Collier, John Loftin, and Anna Wienhard for interesting discussions about this topic, and to the anonymous referees for their useful comments on the first draft of the paper. The mini-course was funded by the UIC NSF RTG grant DMS-1246844, L.P. Schaposnik’s UIC Start-up fund, and NSF DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Higgs Bundles and Geometric Structures on Manifolds Article published earlier |
| spellingShingle | Higgs Bundles and Geometric Structures on Manifolds Alessandrini, D. |
| title | Higgs Bundles and Geometric Structures on Manifolds |
| title_full | Higgs Bundles and Geometric Structures on Manifolds |
| title_fullStr | Higgs Bundles and Geometric Structures on Manifolds |
| title_full_unstemmed | Higgs Bundles and Geometric Structures on Manifolds |
| title_short | Higgs Bundles and Geometric Structures on Manifolds |
| title_sort | higgs bundles and geometric structures on manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210183 |
| work_keys_str_mv | AT alessandrinid higgsbundlesandgeometricstructuresonmanifolds |