# Problem Sheet O

- 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. 🤓

Comments and questions?