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, fiber bundles, fibrations, mapping spaces, loop spaces
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.
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
-
Exercise 7, due June 2, 2025
-
Exercise 8, due June 16, 2025
-
Exercise 9, due June 23, 2025
-
Exercise 10, due June 30, 2025
-
Exercise 11, due July 7, 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 second exam will take place Monday, September 15, 2025, between 13:00-14:30 in Großer Hörsaal, Wegelerstr. 10. The review of the marked exams takes place September 16, between 14:00-15:00 in room 2.008 (Mathematikzentrum).
Instructions for the written exam:
-
During the exam, please have an official picture ID
(national ID card, EU drivers licence, or passport) openly visible at your
place for inspection. We do not need to see your student ID.
- We will provide paper, including scrap paper.
- Coats, jackets, bags and backpacks must be left at the front of the room.
We recommend leaving valuables at home.
- Only writing utensils are allowed at your place during the exam.
In particular, the lecture script, personal notes, or text books are not allowed.
- During the exam, you must not have any wireless devices near or on you.
This includes in particular smart phones, tablets, laptops, and smart watches.
- If we detect any items that are not allowed on you or at your place during the exam, we will view this
as an attempt of fraud, and you fail the exam; it is irrelevant whether or not the forbidden
item or device was actually used.
The first exam took take place July 16, 2025. There were 23 students taking the exam, with the following results:
| Grade |
1,0 |
1,3 |
1,7 |
2,0 |
2,3 |
2,7 |
3,0 |
3,3 |
3,7 |
4,0 |
5,0 |
| No |
5 |
1 |
3 |
1 |
3 |
- |
1 |
1 |
2 |
- |
6 |
S. Schwede, 17.07.2025