Dear everyone
It is (a little past) time to set things in motion with regards to the reading class Introduction to stable homotopy theory.
We will have our first meeting on Thursday next week, and are planning to have a total of four meetings. Here is a preliminary plan for what is to be covered on each meeting. The references below are to Cary Malkiewich's notes.
Meeting 1: Sections 2.1-2.4. Definitions of spectra and their homotopy groups. The stability theorem, which in some sense is the most fundamental property of the category of spectra.
Meeting 2: Sections 2.5-2.6. Generalized homology and cohomology theories. Brown representability theorem + variants. CW spectra.
Meeting 3: Sections 3.1-3.2 The stable homotopy category, different definitions and properties.
Meeting 4: I see two possibilities: Either we talk about sections 3.3-3.4 - homotopy functors, derived functors, or we talk about Sections 4.1-4.2, smash products and duality.
Maybe this schedule is too ambitions, or maybe we can go a little faster and cover both chapters 3 and 4. We will have to see how it goes.
The proposed format is the following: On each meeting there will be a presentation by one or two students, giving a concise summary of the main ideas and results in the relevant sections. The audience is encouraged to ask questions during the presentations, which will hopefully lead to deeper discussion of the material. You are also encouraged to email me ahead of the meetings if you have questions that you would like to see discussed.
So I need one or two volunteers for each meeting to give a presentation on the relevant material. Naturally the most urgent is to have volunteer(s) for next week. Probably you should plan a presentation taking no more than one hour, to leave ample time for discussion. Email me at gregory.arone@math.su.se to let me know if you want to give a presentation and if you have a preference for the week.
Note on credit for the course. As we discussed before, there will be at least one written assignment, and an oral exam at the end. Those who give a presentation do not have to submit the written assignment, though of course you are welcome to do so if you want.
Feel free to write if you have questions or suggestions. I will set up a questions portal on the course webpage, so you can either use that or email me directly.
Best wishes
Greg