This Problem Sheet is based on Lectures 34 and 35.

  • Problem 1 is about reducing a connection..
  • Problem 2 studies the space of connections, and proves that this is an affine space modelled on $ \mathcal{A}^1(M, E)$.
  • Problem 3 relates $d^{ \nabla}$ and $d^{ \nabla^{ \operatorname{Hom}}}$.
  • Problem 4 introduces the idea of a $G$-connection.

Comments and questions?