Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

CANCELLED Non-commutative geometry (NCG)

Practical information
Study year 2016/2017
Block 2
Programme level Full Degree Master
Course responsible
  • Ryszard Nest (5-7470677576426f63766a306d7730666d)
Office: 04.1.09
Phone: +45 35 32 07 28
  • Department of Mathematical Sciences
Course number: NMAK14016U

Course content

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.

Learning outcome

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.

Recommended prerequisites

Elementary knowledge of K-theory, operator algebras and de Rham cohomology.

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MSc Programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


Ryszard Nest


1 block


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Teaching and learning methods

5 lectures and 3 exercise classes per week for 9 weeks,


No limit




Category Hours
Lectures 35
Class Exercises 22
Course Preparation 149
English 206


Type of assessment

Continuous assessment
7 written assignments during the course of which 5 must be approved

Marking scale

passed/not passed

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

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.

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