Geometric Topology (GeomTop)

Course content

Geometric topology is the study of geometric objects, most particularly manifolds, using tools from algebraic topology.  The course covers a  selection of the most important topics within this area, such as Poincaré duality, characteristic classes, and foundations of differential topology.


MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

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 4 hours exercise session per week for 9 weeks.

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
  • parts of the textbook Algebraic Topology by Allen Hatcher.

Algebraic Topology (AlgTop) and Geometry 2 (Geom2) or equivalent is strongly recommended. Advanced Vector spaces (AdVec) and Homological Algebra (HomAlg) or equivalent are also recommended.

Academic qualifications equivalent to a BSc degree are recommended.

Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
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 in-class test, 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 assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 3
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Søren Galatius   (8-6e6873687b707c7a4774687b6f35727c356b72)
Saved on the 14-02-2024

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