MA3405 — Algebraic Topology II (Algebraisk Topologi II)

Spring 2013

Formal Details
Contact Details


Three talented students — Magnus Hellstrøm-Finnsen, Espen Auseth Nielsen, and Erik Rybakken — began the course in January, and all three finished the course with a very well deserved A.

Congratulations to all three of you! Your performances at the exam were very impressive!


The course this year was built around two interwoven themes.

  1. Homotopy theory.
  2. Cohomology and spectral sequence computations.

It was run as follows.

  1. On Monday afternoons I led a meeting from the blackboard. Quite often we also met on Friday afternoons.
  2. The students read up on the ideas introduced in the meetings and wrote up tasks.
  3. I met each student individually two or three times between the end of the meetings and the exam to revise the material.


How can we tell two topological spaces apart? Algebraic topology approaches this question by associating algebraic gadgets to spaces and by developing tools to calculate these algebraic creatures.

These gadgets and tools are enormously rich and diverse, involving all kinds of mathematics — geometric, algebraic, and arithmetic.

Upon successful completion of the course, you will have a strong foundation to build upon in algebraic topology. You will have learnt powerful techniques which will helpful to you whichever your chosen field, and have an understanding of deep ideas which appear in different guises across mathematics and other disciplines.

The experience of participating in this course will be good preparation for those of you intending to pursue higher studies.

Formal details

The course will be taught in English.

The official course description may be found here. However, the contents of this year's course may differ from this.

The course will not follow a specific textbook.

The course builds naturally upon MA3403 Algebraisk Topologi I. It would very likely be possible to follow the course if you have taken MA3204 Homologisk Algebra and another course in topology, say MA3002 Generell Topologi.

It is not necessary to have taken MA3204 Homologisk Algebra. However, if you have taken neither MA3204 nor MA3403, the pace and level of abstraction of the course may be a little too much for you.

Nevertheless, feel free to get in touch if you have a different background and are interested in the course.

Contact Details

You are welcome to contact me by email or to come to my office at any time.

Please feel free to get in touch beforehand if you have any questions about the course.

My email address can be found here.

My office is 1248, Sentralbygg 2. On the door it says Andrew Stacey (i.e. not my name!).

Last updated: 09:46 (GMT+2), 11/06/2013.