NMAK21000U Geometric Topology (GeomTop)

Volume 2024/2025
Education

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

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.

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
  • 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.
4 hours lectures and 4 hours exercise session per week for 9 weeks.
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 134
  • Theory exercises
  • 36
  • Total
  • 206
Written
Oral
Individual
Continuous feedback during the course of the semester
Credit
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.
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 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
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 should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.