NMAK14016U Non-Commutative Geometry (NCG)
MSc Programme in Mathematics
Algebra of compact operators, Fredholm operators and index, the
Toeplitz algebra, reminder on K-theory and the proof of Bott
periodicity, introduction to K-homology.
Elements of periodic cyclic homology, characteristic classes of manifolds and Chern character, Index theorem.
The student will obtain detailed understanding of K-theory and learn basic facts about K-homology, cyclic cohomology and characteristic classes. The student will have a basic understanding of the applications of homological methods for both topological spaces and non-commutative C*-algebras
At the end of the course the student will be able to prove basic properties of topological K-theory and K-homology, demonstrate the ability to compute it in some examples. He/she will have a basic knowledge of yclic theory
The student will be able to use K-theory, K-homology and cyclic homology in both topological and C*-algebraic problems.
- 7,5 ECTS
- Type of assessment
- Continuous assessment7 written assignments during the course of which 5 must be approved
- All aids allowed
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner.
Resubmission of the 7 assignments from the continuous assessment. Deadline 12 noon Friday in the reexamination week. 5 assignments must be approved in order to pass the course.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Class Exercises
- Course Preparation