Algebraic Topology II (AlgTopII)

Course content

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.


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 exercises per week for 9 weeks.

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.

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 3 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, notes, or no electronic aids are allowed for the 3 hours final exam, except for one personally created one-sided A4 page of handwritten notes.

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 4
No limit
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Jesper Grodal   (2-6f6c457266796d33707a336970)
  • Jan Paul Steinebrunner   (3-7076794673677a6e34717b346a71)
Saved on the 11-10-2023

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