NMAA09039U  Algebraic Topology II (AlgTopII)

Volume 2018/2019
Education

MSc Programme in Mathematics

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.

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.
Algebraic Topology (AlgTop) and Homological Algebra (HomAlg), or equivalent.
4 hours lectures and 3 hours exercises per week for 9 weeks.
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Weekly homework counting 50 % towards the grade and a 2 hours 'closed-book' final in-class problem set counting 50 % of the grade.
Aid
Only certain aids allowed

All aids allowed for the weekly homework. No books and no electronic aids are allowed for the 2 hours final exam. Personally created handwritten notes on paper are allowed.

Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam

30 minutes oral examination with no aids or preparation time. The oral examination will cover the entire material of the course, including the exercise sets.

 

Criteria for exam assesment

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

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