Introduction to G2 geometry
The classification of Riemannian manifolds with special holonomy contains two “exceptional” cases: G2 and Spin(7). In this course, I will focus on the G2 case and introduce various topics.
We start from the linear algebra in G2 geometry. Then we study topics such as the torsion of a G2-structure, topological properties of compact manifolds with holonomy contained in G2, the moduli theory, and calibrated geometry.
We start from the linear algebra in G2 geometry. Then we study topics such as the torsion of a G2-structure, topological properties of compact manifolds with holonomy contained in G2, the moduli theory, and calibrated geometry.
Lecturer
Date
17th September ~ 17th December, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-301 | ZOOM 11 | 435 529 7909 | BIMSA |
Prerequisite
Basics of Riemannian geometry, vector bundles and principal bundles, representation theory
Reference
D. D. Joyce, Compact manifolds with special holonomy. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2000. xii+436 pp. ISBN: 0-19-850601-5
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
S. Karigiannis, Deformations of G2 and Spin(7) structures. Canad. J. Math. 57 (2005), no. 5, 1012--1055.
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
S. Karigiannis, Deformations of G2 and Spin(7) structures. Canad. J. Math. 57 (2005), no. 5, 1012--1055.
Audience
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.