This Problem Sheet is based on Lectures 32 and 33

  • Problem 1 explores how to define connections on the tensor product of two bundles.
  • Problem 2 shows how connections behave like tensor derivations (cf. Lecture 18).
  • Problem 3 gives another way of thinking about flat connections. Remark: If you are not familiar with the universal cover, just skip this question.
  • Problem 4 is yet another question about our favourite connection on $TS^n$.
  • Problem 5 discusses left-invariant connections on Lie groups.

Comments and questions?