Categories and Topology (CatTop)

Course content

Topics in algebraic topology centered around the use of categories in homotopy theory and simplicial methods. Topics include simplicial sets, nerves of categories, classifying spaces, homotopy (co)limits, localization and completion.

 

 

Education

MSc Programme in Mathematics

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 3 hours exercises per week for 9 weeks.

In previous years lecture notes were used. It will be aimed to make these notes available from Absalon and/or the lecturers homepage.

AlgTopI and HomAlg or similar. Knowledge of AlgTop1.5 and AlgTopII will be advantageous. (This corresponds roughly to Chapter 1-5 in Hatcher's book Algebraic Topology.)

Academic qualifications equivalent to a BSc degree is recommended.

Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
ECTS
7,5 ECTS
Type of assessment
Continuous assessment
Weekly written exercises. The scores on the weekly written exercises are weighted equally in determining the final grade.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assessment

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

Single subject courses (day)

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