Algebraic Topology of Smooth Manifolds

News

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Credits

You will get a certificate for this class if you attend the example classes regularly and score at least 1 out of 4 points in at least 70% of the homework problems.

It is also possible to take this class as a seminar by replacing the oral exam by a seminar talk; details will be discussed in class.

Homework assignments

Homework problems will be assigned every Friday, starting on April 17. They can be downloaded below and are due on Mondays 10 days later (at any time). You can put your solutions in Diego's mailbox next to 48-210 or upload them as a PDF file in the Submissions tab of the OLAT course. You can submit them in groups of up to 3 students. Of course, in this case everyone should have their fair share both in finding and writing down the solutions; it is expected that everyone can explain their solutions on the blackboard in the example sessions. If you submit your solutions online as a group, only one of you should upload them and indicate the names of all participants on the solution.

• Problem set 1, due April 27
• Problem set 2, due May 4
• Problem set 3, due May 11
• Problem set 4, due May 18
• Problem set 5, due May 25
• Problem set 6, due June 1
• Problem set 7, due June 8
• Problem set 8, due June 15
• Problem set 9, due June 22
• Problem set 10, due June 29

Class Notes

There will be notes for this class that can be downloaded below (if you access this page from the OLAT course).

Disclaimer: As it is the first time this class is offered, this is also the very first version of the notes. There will be errors and inconsistencies. The notes will be changing throughout the semester as material is added, reordered or updated – not drastically, but noticeably. Do not count on the numbers of definitions or propositions being constant in time. The complete notes will not be available from the beginning as they are not finished yet, but I hope to have at least a usable initial version of every chapter ready before it is discussed in class. It should work to download every chapter individually right before it is covered in class, and then stick to this version in case you plan to make annotations for yourself and do not want to replace it later by an updated version.

Of course, I am always happy to get feedback on the notes. So if you find errors or have suggestions on how to improve the notes, please let me know!

Literature

There should be no need to use any further literature besides the notes above. Also, this class does not follow any particular book. However, most of the material covered is quite standard, and it should be easy to find references for it. The following list is a small selection for the beginning:

• A. Hatcher: Algebraic Topology (2021)
• G. Bredon: Topology and Geometry, Springer Graduate Texts in Mathematics 139 (1993)
• R. Bott and L. Tu: Differential Forms in Algebraic Topology, Springer Graduate Texts in Mathematics 82 (1982)

Questions?

If you have any questions – about the organization of the course, the lecture, the homework problems or whatever – do not hesitate to contact us! You can write an e-mail or in the forum, ask Diego (bargans@rptu.de, 48-518), talk to me after the lecture or just come at any time to my office (andreas@rptu.de, 48-517).