This sheet is based on Lectures 11 and 12.

  • Problems 1 and 2 ask you to do some diagram chasing. Such fun! 🎉
  • Problem 3 is another diagram chase. This one is quite hard, but there are pretty colours so that's ok.
  • Problems 4 asks you prove the long exact sequence for a triple of spaces (Hint: Use Problem 3!)
  • Problem 5 asks you to prove the long exact sequence in reduced homology. (This one is much easier.)
  • Problem 5 is about when short exact sequences split.

This is a pretty difficult sheet. 😈

🤓 Feel free to ask a question if you are stuck! 🤓

Comments and questions?