NMAK13011U  K-Theory 2

Volume 2013/2014
MSc programme in Mathematics
Algebra of compact operators, Fredholm operators and index, the Toeplitz algebra, proof of Bott periodicity and axiomatic characterisation of K-theory. Introduction to K-homology
Elements of periodic cyclic homology, characteristic classes of manifolds and chern character.
Learning Outcome
The student will obtain detailed understanding of K-theory and learn basic facts about K-homology, cyclic cohomology and characteristic classes.

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

The student will be able to use K-theory and K-homology in both topological and C*-algebraic problems.
Introduction to K-theory
5 lectures and 3 exercise classes per week for 7 weeks
7,5 ECTS
Type of assessment
Oral examination, 30 min
Exam registration requirements
Approval of three written sets of problems
Written aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners
Criteria for exam assesment
Students has to demonstrate that thay mastered the content of the course
  • Category
  • Hours
  • Lectures
  • 35
  • Theory exercises
  • 21
  • Exam
  • 1
  • Preparation
  • 149
  • Total
  • 206