"Et j'espère que mes neveux me sauront gré,
non seulement des choses que j'ai ici expliquées,
mais aussi de celles que j'ai omises volontairement,
afin de leur laisser le plaisir de les inventer."
René Descartes 

This is the website for the course "Algebraic Topology" (Master) in the summer semester 2023.  
Content 
This is a second course in topology. We will systematically study topological spaces by translating topology into algebra. To do this we will introduce the field of homological algebra. The main topics will be (singular) homology and cohomoloogy, including the MayerVietoris sequence, the universal coefficient theorem and the Künneth theorem, Poincaré duality and applications. In this coures we will assume familiarity with basic concepts from topology as they would be taught in the Bachelor course Topologie at Unversity of Hamburg. The script and exercise sheets will be made available here for anybody who is interested. If you are taking the course for credit you will also need to sign up on Stine. 
Lectures 
Lectures are Tuesdays at 2.15pm in H4 and Thursday at 12.15pm in H3. 
Classes 
Wednesdays at 10.15am in Room 435 there will be an exercise class run by my PhD student Thomas Stempfhuber to discuss solutions to the example sheets. 
Notes 
The complete lecture notes are here. This is the version from 31 July, it may be updated in the future to fix any errors that are found. Please contact me with any comments or corrections! Here is a very short introduction to category theory, based on old notes of mine and extended and edited by Thomas Stempfhuber. Some of you may find this useful as a complement to the lecture notes. 
Exercises 
Exercise sheet 1 (for 12/4/23). Exercise sheet 2 (for 19/4/23). Exercise sheet 3 (for 26/4/23). Exercise sheet 4 (for 3/5/23). Exercise sheet 5 (for 10/5/23). Exercise sheet 6 (for 17/5/23). Exercise sheet 7 (for 31/5/23). Exercise sheet 8 (for 7/6/23). Exercise sheet 9 (for 14/6/23). Exercise sheet 10 (for 21/6/23). Exercise sheet 11 (for 28/6/23). Exercise sheet 12 (for 5/7/23). Exercise sheet 13 (for 12/7/23). 
Office hours 
There are no official office hours planned. I will linger after all lectures to answer questions. You can also contact me by email! 
Exam 
There will be oral exams on 31 July and 1 August, as well as in the week of 9 October. To be admitted to the oral exam you should present solutions in the exercise class three times! There is no other requirement. 