NMAA09039U Algebraic Topology II (AlgTopII)

Volume 2021/2022

MSc Programme in Mathematics


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.

In previous years we have roughly followed Chapter 4 (Homotopy Theory) and Chapter 5 (Spectral Sequences) of Hatcher's book "Algebraic Topology". (This book is available from his website and bookstores.)

Algebraic Topology (AlgTop) and Homological Algebra (HomAlg), or equivalent. (These courses cover the equivalent of Chapter 1 and 2 and parts of Chapter 3 of Hatcher's book "Algebraic Topology".)

Academic qualifications equivalent to a BSc degree is recommended.
4 hours lectures and 4 hours exercises per week for 9 weeks.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • Total
  • 206
Continuous feedback during the course of the semester
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.
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.

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.