NSCPHD1097 Non-commutative geometry (NCG)
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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.
N. Higson, J. Roe Analytic K-homology, Oxford Mathematical monographs, Oxford University Press, 2000.
- Class Exercises
- Course Preparation
Please register at: email@example.com
- 7,5 ECTS
- Type of assessment
- Continuous assessment7 written assignments during the course of which 5 must be approved
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.