NMAK13011U K-Theory 2

Volume 2013/2014
Education
MSc programme in Mathematics
Content
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
Knowledge:
The student will obtain detailed understanding of K-theory and learn basic facts about K-homology, cyclic cohomology and characteristic classes.


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

Competences:
The student will be able to use K-theory and K-homology in both topological and C*-algebraic problems.
Notes
Introduction to K-theory
5 lectures and 3 exercise classes per week for 7 weeks
  • Category
  • Hours
  • Exam
  • 1
  • Lectures
  • 35
  • Preparation
  • 149
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 min
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Exam registration requirements
Approval of three written sets of problems
Aid
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