NSCPHD1097 Non-commutative geometry (NCG)
PLEASE NOTE
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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.
Knowledge:
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
Skills:
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
Competences:
The student will be able to use K-theory, K-homology and cyclic
homology in both topological and C*-algebraic
problems.
Notes,
N. Higson, J. Roe Analytic K-homology, Oxford Mathematical
monographs, Oxford University Press, 2000.
obligatory assignments.
- Category
- Hours
- Class Exercises
- 22
- Course Preparation
- 149
- Lectures
- 35
- Total
- 206
Please register at: rnest@math.ku.dk
- Credit
- 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.
Course information
- Language
- English
- Course code
- NSCPHD1097
- Credit
- 7,5 ECTS
- Level
- Ph.D.
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Natural Sciences PhD Committee
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Ryszard Nest (5-7672697778447165786c326f7932686f)
Phone: +45 35 32 07 28
Lecturers
Ryszard Nest