I am a PhD student in algebraic topology, and I would like to learn something about group cohomology.
The final goal would be to present one or two seminars on this topic, in order to give my mates a gently introduction to this subject and at the same time showing them some striking result/application of this theory. Ideally, my plan for the seminar is:
- Introduce group cohomology, with a lot of motivations and examples
- Explain what makes group cohomology awesome
- Focus on a specific result, and showing some pretty applications of it (something that could be interesting to an algebraic topologist if possible) in order to strenghthen point 2
I am not looking for books, which are already given in these questions:
So my questions are:
- Does anyone know any introductory papers/lecture notes where I can find a concise introduction to group cohomology? I am looking for something which do not contains all the details but which gives me a general view of the main results and applications of the theory. Youtube videos/lecture series are also very welcome. Of course if you want to mention book that are not in the previous answers it is fine aswell.
- Are there any suggestions about results/applications that I can put in points 2 and 3 of the seminar? As I said before the idea is to present this material to other students of algebraic topology, so I would prefer theorems/applications that will appeal to this kind of audience.
EDIT: an answer of this kind References and resources for (learning) chromatic homotopy theory and related areas is also very welcome and pertinent! Thank you in advance, Tommaso