NMAK21000U Geometric Topology (GeomTop)

Volume 2021/2022

MSc Programme in Mathematics


The course covers various topics in the area of algebraic and geometric topology, such as Poincaré duality, characteristic classes, or foundations of differential topology.

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.

Example of course literature:

Introduction to Differential Topology by Bröcker and Jänich, Characteristic Classes by Milnor and Stasheff, Differential Forms in Algebraic Topology by Bott and Tu, and parts of the textbook Algebraic Topology by Allen Hatcher.

Algebraic Topology (AlgTop) or equivalent is strongly recommended. Homological Algebra (HomAlg) or equivalent is also recommended.

Academic qualifications equivalent to a BSc degree are recommended.
4 hours lectures and 3 hours exercise session per week for 9 weeks.
The course is identical to the discontinued course NMAA13029U Algebraic Topology 1.5: Cohomology (AlgTop 1.5). Therefore you cannot register for NMAK21000U - Geometric Topology (GeomTop), if you have already passed NMAA13029U Algebraic Topology 1.5: Cohomology (AlgTop 1.5).
If you are registered with examination attempts in NMAA13029U Algebraic Topology 1.5: Cohomology (AlgTop 1.5) without having passed the course, you have to use your last examination attempts to pass the exam in NMAK21000U - Geometric Topology (GeomTop). You have a total of three examination attempts.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 143
  • Theory exercises
  • 27
  • 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. Only 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 they have mastered the learning outcome of the course.