Chalk "Et j'espère que mes neveux me sauront gré, non seulement des choses que j'ai ici expliquées, mais aussi de celles que j'ai omises volontairement, afin de leur laisser le plaisir de les inventer."

René Descartes

This is the website for the course "Rational Homotopy Theory" (Master) in the winter semester 2020/21.


The study of topological spaces up to homotopy is a deep and notoriously difficult subject. The idea of rational homotopy theory is to simplify the problem by disregarding torsion phenomena, like the finite factors of the cohomology groups and homotopy groups of a space. Quillen and Sullivan developped a beautiful theory of rational homotopy theory, that allows us to describe rational homotopy theory in a completely algebraic way. This works both abstractly (as an equivalence of categories with a certain category of algebras) and concretely (by computing the non-torsion part of many homotopy groups).

To prove our main theorems this course will introduce many algebraic and homotopical tools that are useful throughout topology (and beyond), like simplicial sets, model categories and spectral sequences.

A good background in algebra and topology is highly recommended, as would be the taught in the courses Topologie, Algebra and Algebraic Topology at Unversity of Hamburg.

The script and exercise sheets will be made available here for anybody who is interested.

If you are a Masters student in Hamburg make sure to join the course Moodle once the semester begins. Then you can watch the lectures and participate in classes.

If you are taking the course for credit you will also need to sign up on Stine.


The lectures will be virtual and asynchronous. New lectures will be uploaded twice a week, the links will be available on the course moodle. You can watch the lectures at your own time, pausing, rewinding and forwarding as much as you like. You could watch them alone or with other students.


Once a week there will be an exercise class where we discuss both the solutions to the example sheets and any question you have about the lectures.

We meet on Big Blue Button at 14:15 Monday afternoon. The first meeting is on 2 November. The link will be published on the course Moodle.


Here are the Lecture notes (as of 20 March 2021). Please contact me with any comments or corrections!


The weekly example sheets for the course will appear on Moodle and (with a delay) here.

Sheet 1

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

Sheet 7

Sheet 8

Sheet 9

Sheet 10

Sheet 11

Sheet 12

Sheet 13

Office hours

There is an office half hour 14.15-14.45 on Wednesdays. The link can be found on Moodle. You can also bring your questions to the classes on Monday or send me an email.


There will be oral exams at the end of the semester. I will provide details about this closer to the time.

To be admitted to the oral exam you should present solutions in the exercise class twice!