Algebraic Topology I

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.

Moebius

Topics covered in this course include:

What is algebraic topology?
The fundamental group and covering theory
the Eilenberg-Steenrod axioms
singular (co)homology
cellular (co)homology
classical applications of (co)homology.

This course will be continued in the summer 2016 with the course "Algebraic Topology II", where (co)homology of manifolds will be studied. If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English

Prüfungsbestandteile Oral exam (25 minutes) after the lecture period. Sufficient for the admission to the oral exam is successful participation in the exercise classes (50% of the credits, presentation of a solution in class, active participation).

Bedingungen für einen unbenoteten Leistungsnachweis Oral exam (25 minutes, without grade) after the lecture period. Sufficient for the admission to the oral exam is successful participation in the exercise classes (50% of the credits, presentation of a solution in class, active participation).