Topological K-theory is one of the generalized cohomology theories, and roughly classifies vector bundles over topological spaces. In this lecture, the basic properties of topological K-theory including the Bott periodicity and the Thom isomorphism theorem will be explained. An application will also be provided at the end of the lecture.
-to understand basic properties of topological K-theory.
-to understand an application of topological K-theory.
vector bundles, K-theory, Bott periodicity, Thom isomorphism
|✔ 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 homotopy axiom and the excision axiom||Details will be provided during each class session|
|Class 2||The exactness axiom||Details will be provided during each class session|
|Class 3||The Bott periodicity, I||Details will be provided during each class session|
|Class 4||The Bott periodicity, II||Details will be provided during each class session|
|Class 5||The Thom isomorphism theorem, I||Details will be provided during each class session|
|Class 6||The Thom isomorphism theorem, II||Details will be provided during each class session|
|Class 7||Application||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)