2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Geometry C1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kiyonori Gomi
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (M-102(H115))
- Class
- -
- Course Code
- MTH.B407
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 3Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
to understand basic properties of vector bundles.
to understand a definition of topological K-theory.
Keywords
vector bundles, K-theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | The definition and examples of vector bundles | Details will be provided in class. |
| Class 2 | Basic properties of vector bundles | Details will be provided in class. |
| Class 3 | Subbundle and quotient bundle | Details will be provided in class. |
| Class 4 | Vector bundles on compact Hausdorff spaces, I | Details will be provided in class. |
| Class 5 | Vector bundles on compact Hausdorff spaces, II | Details will be provided in class. |
| Class 6 | A definition of K-theory | Details will be provided in class . |
| Class 7 | Product in K-theory | Details will be provided in class. |
Study advice (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)
No textbook is set.
Lecture note will be provided.
Reference books, course materials, etc.
M. F. Atiyah, K-theory. Lecture notes by D. W. Anderson W. A. Benjamin, Inc., New York-Amsterdam 1967
Evaluation methods and criteria
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.A202 ： Introduction to Algebra II
- MTH.A203 ： Introduction to Algebra III
- MTH.A204 ： Introduction to Algebra IV
- MTH.A204 ： Introduction to Algebra IV
Prerequisites
require proficiency in basic topology and algebra.