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.