Principal Bundles, Connections, and Holonomy
In this course, we give a detailed introduction to the theory of principal bundles. After defining principal bundles, we introduce connections and holonomy groups on them, and compare these notions with the corresponding theory of vector bundles. We then present the classification of holonomy groups of Riemannian manifolds and discuss the geometric structures appearing in the classification. If time permits, we will also cover the theory of characteristic classes via Chern-Weil theory.
讲师
日期
2026年02月25日 至 05月13日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 15:20 - 18:40 | A3-4-312 | ZOOM 11 | 435 529 7909 | BIMSA |
修课要求
vector bundles and their connections, basics of Riemannian manifolds
参考资料
D. D. Joyce, Riemannian holonomy groups and calibrated geometry. Oxford Graduate Texts in Mathematics, 12. Oxford University Press, Oxford, 2007. x+303 pp. ISBN: 978-0-19-921559-1
H. Konno, [Differential geometry] Bibun kikagaku (in Japanese), University of Tokyo Press, 2013.
H. Konno, [Differential geometry] Bibun kikagaku (in Japanese), University of Tokyo Press, 2013.
听众
Advanced Undergraduate
, Graduate
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Kotaro Kawai于日本东京大学取得学士和硕士学位，并于2013年在日本东北大学博士毕业。此前他以助理教授身份就职于日本学习院大学，学习院大学是日本皇家高等学府，著名教授小平邦彦也在此就职。他于2022年加入BIMSA任副研究员。Kawai主要研究方向是的主要研究方向是微分几何，具体为有例外和乐的流形。