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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| 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/123456789/210183 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Higgs Bundles and Geometric Structures on Manifolds / D. Alessandrini // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 42 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |