This sheet is based on Lectures 15 and 16.

  • Problem 1 is easy but you will probably all find it hard as it's been nearly six weeks since we did the fundamental group (so chances are you've forgotten it all ...)
  • Problem 2 is an easy question about a commuting hexagon. It's called the Hexagon Lemma. Surprise.
  • Problems 3 and 4 are famous theorems that are very easy to prove given the fact that an odd map has odd degree (Theorem 15.12 from today's lecture.)
  • Problems 5 and 6 are both very easy once you decode the notation. (Well, okay, 6 is a bit harder.)

Despite me claiming that every question is easy, this is probably quite a challenging sheet. Feel free to ask questions if you are stuck! 😀

Comments and questions?