Topology II (V3D2), summer term 2025

Mondays, 14:15-16:00 Kleiner Hörsaal, and Wednesdays, 8:15-10:00, Großer Hörsaal (Wegelerstr. 10)

Lecturer: Stefan Schwede
Email : schwede (at) math.uni-bonn.de
Assistant: Tobias Lenz
Email: lenz (at) math.uni-bonn.de

Topics

cohomology, cup product, Künneth theorems, manifolds, orientations, Poincaré duality

Literature:
- G. Bredon, Topology and Geometry (Springer)
- A. Hatcher, Algebraic Topology
- T. tom Dieck, Algebraic topology (EMS Textbooks in Mathematics)

Prerequisites

This class is a direct continuation of my class "Topology I" from the winter term 2024/25. Prerequisites are point set topology (topological spaces, subspaces, quotient spaces, compactness, separation axioms); fundamental group; covering space theory; CW-complexes; higher homotopy groups; singular and cellular homology

Additional resources

I previously taught this class in the summer term 2021 during the covid pandemic. I have made the slides and videos that I produced then available on eCampus, so that they can serve as additional resources. To access the slides and videos, you must join the eCampus course "V3D2/F4D1 - Topologie II / Topology II". The contents may differ to some extent from the content of the videos.

Evaluation of the class

The evaluation of this class will take place June 2, 2025, during the class.

Exercises

We provide weekly exercise sheets on Fridays, available here for download. The completed exercises have to be handed in 10 days later before the Monday lecture. Exercise sheets may be handed in jointly by at most three students.

Exercise 1, due April 21, 2025
Exercise 2, due April 28, 2025
Exercise 3, due May 5, 2025
Exercise 4, due May 12, 2025
Exercise 5, due May 19, 2025
Exercise 6, due May 26, 2025

Time (c.t.)/Place	Tutor
Tuesdays 8, SR 0.008	Constantin Gurdon
Tuesdays 12, SR 1.007	Yehor Avdieiev
Thursdays 8, SR 0.008	Yordan Toshev

Exam

The prerequisites for admission to the exam are:

to score at least 50% of the points for the exercises
to present at least two solutions to exercises during the course of the term.

The first exam will take place Wednesday, July 16, 2025, between 8:30--10:00 in Großer Hörsaal (Wegelerstr. 10). The review of the marked exams takes place July 17, between 14:00-15:00.

The second exam will take place Monday, September 15, 2025.

S. Schwede, 20.05.2025