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.
Lecturer
Date
25th February ~ 13th May, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 15:20 - 18:40 | A3-4-312 | ZOOM 11 | 435 529 7909 | BIMSA |
Prerequisite
vector bundles and their connections, basics of Riemannian manifolds
Reference
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.
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Kotaro Kawai got a bachelor's degree and a master's degree from the university of Tokyo, and received his Ph.D from Tohoku university in 2013. He was an assistant professor at Gakushuin university in Japan, then he moved to BIMSA in 2022. His research interests are in differential geometry, focusing on manifolds with exceptional holonomy.