Rational Homotopy Theory

Winter Semester 2020/21

This is the website for the course “Rational Homotopy Theory” (Master) in the Winter Semester 2020/21.

Content

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 Universität 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.