ALGEBRAIC TOPOLOGY CLASS

• This semester again the exam will be held on zoom individually. After we scheduled a time slot I will send you an invitation link just as for the class. Both of us will have our video and audio on, but, of course, there will be no recording. 

• Before the exam starts you will have to show your photo id to verify your identity and you will need to agree to the format of the exam;

• As a start, I will ask you about a wider topic (e.g. basic definition. and properties of the fundamental group, the fundamental group of the circle, covering spaces, Mayer Vietoris sequence, cup product in cohomology,...) and after a couple of minutes of thinking you should start to present the main definitions, theorems and lemmas in the given topic, I will ask questions on the way and specify if you should go into more details.

• Once we have discussed the first topic I will ask narrower questions about some of the other topics (e.g. state and prove the Brower fixed point theorem, what is the main idea in the proof of Excision, how do you compute the homology of a sphere), these could include simple exercises, computations, generally easier than the one from the exercise session. You are not expected to be able to solve all the exercises without help, but you should be able to start working on them and finish them with my help. I expect that all of this will take about an hour. 

• You are not allowed to use any help (oral, online or written, ...) during the exam, and I have to terminate the exam if I suspect that any illegal aids have been used.

• In the exam, you might need to draw pictures or write formulas. You should prepare a way to do this. Here are some suggestions:

  • zoom has an integrated whiteboard, that you can use moderately well even with a mouse or a touchpad (if you need it, I could send you an invitation to an empty practice room before the exam);

  • you can use white paper with a thick and dark pen, and show it to the camera, or send it to me as a file through email;

  • if you have a blackboard or whiteboard at home you can direct your camera to it. 

       

       Please let me know what option you are planning to use ahead of time.

• ​If the internet connection turns out to be insufficient for the exam we will communicate by email to figure out a good solution.

• I know, that this is a hard and unusual situation for all of us. Let me know if you have complications, or if you need help, and we will make it work. 

• Here is a link with useful tips from the University on how to prepare for the exam. Please read it before the exam.  

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Stay safe, and as usual ask questions!

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