I'm looking for a textbook on the differential geometry of fibre bundles containing a not too brief discussion of the following topics:
- Principal and associated bundles, (reduction of) structure groups.
- Ehresmann connections and their curvature
- Other common definitions of a connection on a bundle and various ways of organizing that information (connection forms etc.)
- Holonomy, mondromy and gauge groups
- Yang-Mils functionals
- Foliations and their holonomy
- Jet bundles
Is there such a textbook? (By which i mean a book that contains exercise problems).
If not, where can i find problem sets for these topics?
Best Answer
A standard great reference textbook with exercises is definitely Husemöller's "Fiber bundles", especially Part I and III for your needs. It covers most of your topics (I don't think there is a book covering all of your topics in a great way, so I am convinced that this one should be the perfect fit, as it covers most of them in a great way). There is also good stuff to say about the lecture notes of Koszul, but they are without exercises.