Time and Place: Mo 10:15-12:00 - Kleiner Hörsaal; We 8:15-10:00 - Kleiner Hörsaal

Content

This lecture course is the last part of a series of five lecture courses about topology. It will cover the following topics with emphasis on the third one:

Bordism Theory
Pontrjagin Thom construction
Spectral sequences and their applications to (co-)homology and homotopy
Principal G-bundles and characteristic classes
Group (co-)homology

To follow the course, one has to be familiar with the material covered in the previous courses Algebraic Topology 1 (Winter 24/25) and Topology 2 (Summer 24).

Literature

We will not be following a specific book. There are many good sources, e.g.:

Hatcher: Algebraic topology
tom Dieck: Algebraic topology
Switzer: Algebraic toplogy - homotopy and homology
Weibel: An introduction to homological algebra
Whitehead: Elements of homotopy theory

We will provide lecture notes for the course.

Exams

There will be oral exams at the end of the course. The first round is scheduled for July 14 - July 24 and the second round for August 19 - August 22.

Exercises

There will be weekly exercise sheets, which the students can submit in teams of at most three. The solutions will partially be discussed in the tutorials. To be admitted to the final exam, students have to collect at least 50% of possible points on the exercise sheets and sucessfully present the solution to one of the exercises in the tutorial.