This Problem Sheet covers Lectures 38, 39, 40, and 41.

• Problem 1 was used in the proof of the Bianchi Identity.
• Problem 2 was used in the proof of Theorem 40.9 and also in the proof of the Ambrose-Singer Holonomy Theorem.
• Problem 3 was used in the proof of Theorem 40.6.
• Problem 4 relates holonomy on principal bundles to holonomy on vector bundles.
• Problem 5 clarifies the notion of a $G$-connection from Problem Sheet Q.
• Problem 6 asks you to derive the vector-bundle version of the Bianchi Identity from the principal bundle version.
• Problem 7 asks you to derive the vector bundle version of the Ambrose Singer Holonomy Theorem from the prinicpal bundle version.
• Problem 8 is just for fun. 🤓