The most basic characteristic classes of vector bundles are introduced. Their basic properties and applications are also explained.
- to understand a definition and properties of the most basic characteristic classes of vector bundles.
- to learn applications of these characterisitic classes.
vector bundle, Euler class, Stiefel-Whiteny class, Chern class, Pontryagin class, index theorem, exotic sphere
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course.
Course schedule | Required learning | |
---|---|---|
Class 1 | Thom class and Euler class | Details will be provided during each class session |
Class 2 | Applications of Euler class | Details will be provided during each class session |
Class 3 | Stiefel-Whiteny class | Details will be provided during each class session |
Class 4 | Chern class | Details will be provided during each class session |
Class 5 | Pontryagin class | Details will be provided during each class session |
Class 6 | Index theorem | Details will be provided during each class session |
Class 7 | Exiotic sphere | Details will be provided during each class session |
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
non required
John Milnor, James D. Stasheff, Characteristic Classes. Volume 76 (Annals of Mathematics Studies), Princeton University Press.
Ichiro Tamura, Differential Topology, Iwanami.
Assignments (100%).
Knowledge on topology (MTH.B341) and maniofolds (MTH.B301, MTH.B302) are required. Also, students are supposed to have attended Advanced topics in Geometry A(MTH.B401) or Advanced courses in Geometry A(ZUA.B331).