Algebraic Topology I (V4D1), winter term 2025/26

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

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

Topics

Hurewicz theorem, Blakers-Massey theorem, Eilenberg-MacLane spaces, representability of singular cohomology, CW-approximation, geometric realization, spaces versus simplicial sets

Literature:
- F. Waldhausen, Algebraische Topologie II (script, in german)
- G. Bredon, Topology and Geometry (Springer)
- A. Hatcher, Algebraic Topology (Cambridge University Press)
- T. tom Dieck, Algebraic topology (EMS Textbooks in Mathematics)
- S. Schwede, Kohomologie (script, in german)
- S. Schwede, Spaces versus simplicial sets (script)

Prerequisites

This class is a continuation of my class "Topology II" from the summer term 2025. Prerequisites are point set topology, fundamental group, covering space theory, CW-complexes, higher homotopy groups, singular homology and cohomology, cup product, Künneth and unviersal coefficient theorems, manifolds, Poincaré duality, fiber bundles, Serre fibrations, mapping spaces, loop spaces.

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.

There are three exercise groups, all meeting in SR 0.006 in the Mathematikzentrum (Endenicher Allee 60). The first meeting of the groups are during the second week of classes, i.e., starting October 20, 2025

Time	Tutor
Mondays, 16-18
Tuesdays, 8-10
Wednesdays, 14-16

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 written exam will take place February 4, 2026. The second exam will take place on March 24, 2026.

S. Schwede, 30.07.2025