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. 🤓

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