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- Academic unit or major
- Mathematics
- Instructor(s)
- Gomi Kiyonori
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri5-6(H119A)
- Group
- -
- Course number
- ZUA.B331
- Credits
- 1
- Academic year
- 2021
- Offered quarter
- 1Q
- Syllabus updated
- 2021/3/19
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
Topological K-theory is one of the generalized cohomology theories, and roughly classifies vector bundles over topological spaces. This lecture start with an exposition the definition and basic properties of vector bundles, and then introduces topological K-theory.
Student learning outcomes
-to understand basic properties of vector bundles.
-to understand a definition of topological K-theory.
Keywords
vector bundles, topological K-theory
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 | Basic properties of vector bundles | Details will be provided during each class session |
| Class 2 | Basic properties of vector bundles | Details will be provided during each class session |
| Class 3 | Subbundle and quotient bundle | Details will be provided during each class session |
| Class 4 | Vector bundles on compact Hausdorff spaces, I | Details will be provided during each class session |
| Class 5 | Vector bundles on compact Hausdorff spaces, II | Details will be provided during each class session |
| Class 6 | A definition of K-theory | Details will be provided during each class session |
| Class 7 | Product in K-theorys | 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.
M. F. Atiyah, K-theory. Lecture notes by D. W. Anderson W. A. Benjamin, Inc., New York-Amsterdam 1967
Assessment criteria and methods
Assignments (100%).
Related courses
- MTH.B203 ： Introduction to Topology III
- MTH.B204 ： Introduction to Topology IV
- MTH.B341 ： Topology
- LAS.M106 ： Linear Algebra II
- MTH.A201 ： Introduction to Algebra I
- MTH.A203 ： Introduction to Algebra III
- MTH.A204 ： Introduction to Algebra IV
Prerequisites (i.e., required knowledge, skills, courses, etc.)
require proficiency in basic topology (MTH.B203, MTH.B204, MTH.B341) and algebra (LAS.M106, MTH.A201, MTH.A202, MTH.A203, MTH.A204)
