Algebraic Topology, WS 2018/19

Prof. Dr. C. Löh / D. Fauser / J. Witzig


Algebraic Topology

Algebraic topology studies topological spaces via algebraic invariants -- by modelling certain aspects of topological spaces in the realm of algebra, e.g., by groups and group homomorphisms. Classical examples include homotopy groups and (co)homology theories.


Algebraic topology has various applications, both in theoretical and in applied mathematics, for instance, through fixed point theorems and (non-)embeddability results. For example, Nash's proof of existence of certain equilibria in game theory is based on a topological argument. Topics covered in this course include: This course will be complemented with the course "Group Cohomology" in the summer 2019, where (co)homology of groups will be studied. The course in SS 2019 can also be attended independently of the present course on Algebraic Topology.

If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English.

Lecture notes: pdf. Topics covered so far: