• Problems 1, 3 and 4 are about vector-valued wedge products.
• Problems 2 and 5 are about fundamental vector fields.
• Problem 6 relates holonomy on principal bundles to holonomy on vector bundles.
• Problem 7 clarifies the notion of a $G$-connection from Problem Sheet N.
• Problem 8 asks you to derive the vector-bundle version of the Bianchi Identity from the principal bundle version.
• Problem 9 asks you to derive the vector bundle version of the Ambrose Singer Holonomy Theorem from the prinicpal bundle version.
• Problem 10 is just for fun. 🤓