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.
-to understand basic properties of vector bundles.
-to understand a definition of topological K-theory.
vector bundles, topological K-theory
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
A standard lecture course.
|Course schedule||Required learning|
|Class 1||The definition and examples 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|
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.
No textbook is set.
Lecture note will be provided.
M. F. Atiyah, K-theory. Lecture notes by D. W. Anderson W. A. Benjamin, Inc., New York-Amsterdam 1967
require proficiency in basic topology (MTH.B203, MTH.B204, MTH.B341) and algebra (LAS.M106, MTH.A201, MTH.A202, MTH.A203, MTH.A204)