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- Academic unit or major
- Mathematics
- Instructor(s)
- Gomi Kiyonori
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue3-4(H104)
- Group
- -
- Course number
- ZUA.B332
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 2Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
The most basic characteristic classes of vector bundles are introduced. Their basic properties and applications are also explained.
Student learning outcomes
- to understand a definition and properties of the most basic characteristic classes of vector bundles.
- to learn applications of these characterisitic classes.
Keywords
vector bundle, Euler class, Stiefel-Whiteny class, Chern class, Pontryagin class, index theorem, exotic sphere
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course.
Course schedule/Required learning
| 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 |
Out-of-Class Study Time (Preparation and Review)
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.
Textbook(s)
non required
Reference books, course materials, etc.
John Milnor, James D. Stasheff, Characteristic Classes. Volume 76 (Annals of Mathematics Studies), Princeton University Press.
Ichiro Tamura, Differential Topology, Iwanami.
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B341 ： Topology
- MTH.B301 ： Geometry I
- MTH.B302 ： Geometry II
- ZUA.B331 ： Advanced courses in Geometry A
- MTH.B401 ： Advanced topics in Geometry A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
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).
