NMAA13034U Introduction to K-theory (K-Theory)
The course will contain the following specific elements:
- Projections in C^*-algebras and vector bundles
- The Grassmannian and classification of vector bundles
- The Grothendieck construction af K-theory
- Exact sequences and calculation of K-groups.
- K-theory of C_0(X) and Thom isomorphism
- Atiyah's KR-theory.
The course is intended both for student in Non-commutative geometry and students in Topology. A successor to the course will stress the analytic aspects of K-theory, like the proof of the periodicity theorem, index theory etc.
Knowledge: The student will obtain knowledge of the elements mentioned in the description of the content
Skills: After completing the course the student will be able to
1. calculate K-groups
2. classify projections in C^*-algebras and vector bundles
3. translate between the C^*-algebra and the vector bundle approach
After completing the course the student will be able to
1. prove theorems within the subject of the course
2. apply the theory to both topology and non-commutative geometry
3. understand the extensive litterature on elementary K-theory and to read the more advanced parts of the subject.
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- 7,5 ECTS
- Type of assessment
- Continuous assessmentEvaluation during the course of 7 compulsory activities.
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner.
- Oral, 45 minutes. Several internal examiners.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Theory exercises