Algebraic Topology 1 (V4D1), WS 2023/34

Lecturer: Markus Hausmann (
Assistent: Elizabeth Tatum (


Mondays, 14:15 - 16:00 and Fridays 14:15 - 16:00 in Kleiner Hörsaal, Wegelerstr. 10

Evaluation questionnaire (Veranstaltungskennung V4D1, Password in the lecture on Friday, December 1st. If you cannot make it to the lecture, please send me an email at [Link]

Topics : Serre spectral sequence and applications (rational homotopy groups of spheres, cohomology of Eilenberg-MacLane spaces), Thom isomorphisms, characteristic classes, bordism theory.
Prerequisites : A good understanding of (co-)homology of spaces and some homotopy theory (e.g., Serre fibrations), as for example covered by the courses Topology I + II.

Exam : February 2nd, 2024, 14:00-16:00
Reexam : March 19th, 2024, 9:00-11:00

Exercise sessions

Exercise groups meet once per week, at the dates shown below. The sessions start in the second week of the semester (from October 16 on).

Please sign up for an exercise group during the first lecture on October 9th. If you have questions about the exercise sessions, please contact your tutor or the assistent Elizabeth Tatum.

There will be weekly exercise sheets. They will be posted on this website on Mondays, and are to be handed in on Friday the week after (either during the lecture or by email to your tutor). The first exercise sheet will be handed in at the start of the semester, and should be handed in on Friday October 20th.

You can hand in in groups of up to three students. Your write-ups will be graded by your tutor, and solutions will be discussed during the exercise sessions.

You need to receive at least 50% of the exercise points to qualify for the exam.


Allen Hatcher: Spectral sequences in algebraic topology, available here: [Link]
Robert Mosher, Martin Tangora: Cohomology operations and applications in homotopy theory.
John McCleary: A User's guide to spectral sequences
John Milnor, James Stasheff: Characteristic classes

Exercise sheets

[Homework 1]
[Homework 2]
[Homework 3]
[Homework 4]
[Homework 5 (with added finite type hypothesis in Problem 2)]
[Homework 6]
[Homework 7]
[Homework 8]

Group Time and location Tutor
1 Mon 8-10 R0.006 Phil Pützstück
2 Mon 16-18 R0.006 Anton Engelmann
3 Tue 10-12 R0.006 Lucas Piessevaux
4 Wed 8-10 R0.006 Julius Groenjes