Algebraic Topology II (AlgTopII)

Course content

This course will be an introduction to homotopy theory and spectral sequences. The first part will focus on elementary homotopy theory covering e.g., fibrations, cofibrations, cellular approximation, Whitehead and Hurewich theorem. The second part will focus on spectral sequences in homotopy theory. The Serre spectral sequence is constructed and used to calculate homology and homotopy groups of a number of interesting spaces.

Education

MSc Programme in Mathematics

Learning outcome
  • Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.
  • Skills: To be able to use the acquired knowledge to perform computations.
  • Competencies: To be able to produce independent proofs in extension of the acquired knowledge.

4 hours lectures and 3 hours exercises per week for 9 weeks.

Algebraic Topology (AlgTop) and Homological Algebra (HomAlg), or equivalent.

ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Weekly homework (each weighted equally, accounting for 70% of the grade) and a final in-class problem set (accounting for 30% of the grade). You will have three hours for the in-class problem set.
Aid
Written aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Criteria for exam assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 143
  • Lectures
  • 36
  • Theory exercises
  • 27
  • English
  • 206